Which of the following is a multiple of 75 closest to 200?
150
225
175
200
of 10
Multiples of 75
Multiples of 75
Multiples of 75 are numbers expressed as 75×𝑛, where 𝑛 is an integer. These multiples are not always even; they follow a pattern, increasing by 75 each time (e.g., 75, 150, 225, 300, 375). Multiples of 75 are crucial in mathematics, especially in algebraic concepts, squares, square roots, and fractions. They are fundamental for understanding number properties and performing various arithmetic operations efficiently. Recognizing these multiples aids in grasping complex mathematical ideas and solving algebraic equations. Multiples serve as essential building blocks in number theory, helping explore patterns, relationships, and the behavior of numbers within mathematical frameworks. This understanding is key to mastering more advanced mathematical concepts and applications.
What are Multiples of 75?
Multiples of 75 are numbers that can be expressed as 75×n, where n is an integer. These numbers are always even and include values like 75 , 150, 225, 300, and so on.
Prime Factorization of 75 :3 x 5 x 5
First 10 Multiples of 75 are 75, 150, 225, 300, 375, 450, 525, 600, 675, 750.
First 50 Multiples of 50 are 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, 900, 975, 1050, 1125, 1200, 1275, 1350, 1425, 1500, 1575, 1650, 1725, 1800, 1875, 1950, 2025, 2100, 2175, 2250, 2325, 2400, 2475, 2550, 2625, 2700, 2775, 2850, 2925, 3000, 3075, 3150, 3225, 3300, 3375, 3450, 3525, 3600, 3675, 3750.
For example, 75, 150, 225 and 300 are all multiples of 75, 140 is not a multiple of 75 for the following reasons:
| Number | Reason | Remainder |
|---|---|---|
| 75 | 75 is 75×175×1, which makes it a multiple of 75 | 0 |
| 150 | 150 is 75×275×2, which makes it a multiple of 75 | 0 |
| 225 | 225 is 75×375×3, which makes it a multiple of 75 | 0 |
| 300 | 300 is 75×475×4, which makes it a multiple of 75 | 0 |
| 140 | 140 is not divisible by 75, 140 ÷ 75 = 1 with a remainder of 65 | 65 |
List of First 100 Multiples of 75 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 75 | 75 is 75×175×1, which makes it a multiple of 75 | 0 |
| 150 | 150 is 75×275×2, which makes it a multiple of 75 | 0 |
| 225 | 225 is 75×375×3, which makes it a multiple of 75 | 0 |
| 300 | 300 is 75×475×4, which makes it a multiple of 75 | 0 |
| 375 | 375 is 75×575×5, which makes it a multiple of 75 | 0 |
| 450 | 450 is 75×675×6, which makes it a multiple of 75 | 0 |
| 525 | 525 is 75×775×7, which makes it a multiple of 75 | 0 |
| 600 | 600 is 75×875×8, which makes it a multiple of 75 | 0 |
| 675 | 675 is 75×975×9, which makes it a multiple of 75 | 0 |
| 750 | 750 is 75×1075×10, which makes it a multiple of 75 | 0 |
| 825 | 825 is 75×1175×11, which makes it a multiple of 75 | 0 |
| 900 | 900 is 75×1275×12, which makes it a multiple of 75 | 0 |
| 975 | 975 is 75×1375×13, which makes it a multiple of 75 | 0 |
| 1050 | 1050 is 75×1475×14, which makes it a multiple of 75 | 0 |
| 1125 | 1125 is 75×1575×15, which makes it a multiple of 75 | 0 |
| 1200 | 1200 is 75×1675×16, which makes it a multiple of 75 | 0 |
| 1275 | 1275 is 75×1775×17, which makes it a multiple of 75 | 0 |
| 1350 | 1350 is 75×1875×18, which makes it a multiple of 75 | 0 |
| 1425 | 1425 is 75×1975×19, which makes it a multiple of 75 | 0 |
| 1500 | 1500 is 75×2075×20, which makes it a multiple of 75 | 0 |
| 1575 | 1575 is 75×2175×21, which makes it a multiple of 75 | 0 |
| 1650 | 1650 is 75×2275×22, which makes it a multiple of 75 | 0 |
| 1725 | 1725 is 75×2375×23, which makes it a multiple of 75 | 0 |
| 1800 | 1800 is 75×2475×24, which makes it a multiple of 75 | 0 |
| 1875 | 1875 is 75×2575×25, which makes it a multiple of 75 | 0 |
| 1950 | 1950 is 75×2675×26, which makes it a multiple of 75 | 0 |
| 2025 | 2025 is 75×2775×27, which makes it a multiple of 75 | 0 |
| 2100 | 2100 is 75×2875×28, which makes it a multiple of 75 | 0 |
| 2175 | 2175 is 75×2975×29, which makes it a multiple of 75 | 0 |
| 2250 | 2250 is 75×3075×30, which makes it a multiple of 75 | 0 |
| 2325 | 2325 is 75×3175×31, which makes it a multiple of 75 | 0 |
| 2400 | 2400 is 75×3275×32, which makes it a multiple of 75 | 0 |
| 2475 | 2475 is 75×3375×33, which makes it a multiple of 75 | 0 |
| 2550 | 2550 is 75×3475×34, which makes it a multiple of 75 | 0 |
| 2625 | 2625 is 75×3575×35, which makes it a multiple of 75 | 0 |
| 2700 | 2700 is 75×3675×36, which makes it a multiple of 75 | 0 |
| 2775 | 2775 is 75×3775×37, which makes it a multiple of 75 | 0 |
| 2850 | 2850 is 75×3875×38, which makes it a multiple of 75 | 0 |
| 2925 | 2925 is 75×3975×39, which makes it a multiple of 75 | 0 |
| 3000 | 3000 is 75×4075×40, which makes it a multiple of 75 | 0 |
| 3075 | 3075 is 75×4175×41, which makes it a multiple of 75 | 0 |
| 3150 | 3150 is 75×4275×42, which makes it a multiple of 75 | 0 |
| 3225 | 3225 is 75×4375×43, which makes it a multiple of 75 | 0 |
| 3300 | 3300 is 75×4475×44, which makes it a multiple of 75 | 0 |
| 3375 | 3375 is 75×4575×45, which makes it a multiple of 75 | 0 |
| 3450 | 3450 is 75×4675×46, which makes it a multiple of 75 | 0 |
| 3525 | 3525 is 75×4775×47, which makes it a multiple of 75 | 0 |
| 3600 | 3600 is 75×4875×48, which makes it a multiple of 75 | 0 |
| 3675 | 3675 is 75×4975×49, which makes it a multiple of 75 | 0 |
| 3750 | 3750 is 75×5075×50, which makes it a multiple of 75 | 0 |
| 3825 | 3825 is 75×5175×51, which makes it a multiple of 75 | 0 |
| 3900 | 3900 is 75×5275×52, which makes it a multiple of 75 | 0 |
| 3975 | 3975 is 75×5375×53, which makes it a multiple of 75 | 0 |
| 4050 | 4050 is 75×5475×54, which makes it a multiple of 75 | 0 |
| 4125 | 4125 is 75×5575×55, which makes it a multiple of 75 | 0 |
| 4200 | 4200 is 75×5675×56, which makes it a multiple of 75 | 0 |
| 4275 | 4275 is 75×5775×57, which makes it a multiple of 75 | 0 |
| 4350 | 4350 is 75×5875×58, which makes it a multiple of 75 | 0 |
| 4425 | 4425 is 75×5975×59, which makes it a multiple of 75 | 0 |
| 4500 | 4500 is 75×6075×60, which makes it a multiple of 75 | 0 |
| 4575 | 4575 is 75×6175×61, which makes it a multiple of 75 | 0 |
| 4650 | 4650 is 75×6275×62, which makes it a multiple of 75 | 0 |
| 4725 | 4725 is 75×6375×63, which makes it a multiple of 75 | 0 |
| 4800 | 4800 is 75×6475×64, which makes it a multiple of 75 | 0 |
| 4875 | 4875 is 75×6575×65, which makes it a multiple of 75 | 0 |
| 4950 | 4950 is 75×6675×66, which makes it a multiple of 75 | 0 |
| 5025 | 5025 is 75×6775×67, which makes it a multiple of 75 | 0 |
| 5100 | 5100 is 75×6875×68, which makes it a multiple of 75 | 0 |
| 5175 | 5175 is 75×6975×69, which makes it a multiple of 75 | 0 |
| 5250 | 5250 is 75×7075×70, which makes it a multiple of 75 | 0 |
| 5325 | 5325 is 75×7175×71, which makes it a multiple of 75 | 0 |
| 5400 | 5400 is 75×7275×72, which makes it a multiple of 75 | 0 |
| 5475 | 5475 is 75×7375×73, which makes it a multiple of 75 | 0 |
| 5550 | 5550 is 75×7475×74, which makes it a multiple of 75 | 0 |
| 5625 | 5625 is 75×7575×75, which makes it a multiple of 75 | 0 |
| 5700 | 5700 is 75×7675×76, which makes it a multiple of 75 | 0 |
| 5775 | 5775 is 75×7775×77, which makes it a multiple of 75 | 0 |
| 5850 | 5850 is 75×7875×78, which makes it a multiple of 75 | 0 |
| 5925 | 5925 is 75×7975×79, which makes it a multiple of 75 | 0 |
| 6000 | 6000 is 75×8075×80, which makes it a multiple of 75 | 0 |
| 6075 | 6075 is 75×8175×81, which makes it a multiple of 75 | 0 |
| 6150 | 6150 is 75×8275×82, which makes it a multiple of 75 | 0 |
| 6225 | 6225 is 75×8375×83, which makes it a multiple of 75 | 0 |
| 6300 | 6300 is 75×8475×84, which makes it a multiple of 75 | 0 |
| 6375 | 6375 is 75×8575×85, which makes it a multiple of 75 | 0 |
| 6450 | 6450 is 75×8675×86, which makes it a multiple of 75 | 0 |
| 6525 | 6525 is 75×8775×87, which makes it a multiple of 75 | 0 |
| 6600 | 6600 is 75×8875×88, which makes it a multiple of 75 | 0 |
| 6675 | 6675 is 75×8975×89, which makes it a multiple of 75 | 0 |
| 6750 | 6750 is 75×9075×90, which makes it a multiple of 75 | 0 |
| 6825 | 6825 is 75×9175×91, which makes it a multiple of 75 | 0 |
| 6900 | 6900 is 75×9275×92, which makes it a multiple of 75 | 0 |
| 6975 | 6975 is 75×9375×93, which makes it a multiple of 75 | 0 |
| 7050 | 7050 is 75×9475×94, which makes it a multiple of 75 | 0 |
| 7125 | 7125 is 75×9575×95, which makes it a multiple of 75 | 0 |
| 7200 | 7200 is 75×9675×96, which makes it a multiple of 75 | 0 |
| 7275 | 7275 is 75×9775×97, which makes it a multiple of 75 | 0 |
| 7350 | 7350 is 75×9875×98, which makes it a multiple of 75 | 0 |
| 7425 | 7425 is 75×9975×99, which makes it a multiple of 75 | 0 |
| 7500 | 7500 is 75×10075×100, which makes it a multiple of 75 | 0 |
Read More About Multiples of 75
Important Notes
Even Numbers: All multiples of 75 are numbers that end in 00 or 75 (e.g., 75, 150, 225, 300).
Divisibility: A number is a multiple of 75 if it can be divided by 75 with no remainder.
Factors: Multiples of 75 have 75 as one of their factors.
Infinite Sequence: There are infinitely many multiples of 75, extending indefinitely as 75, 150, 225, 300, 375, and so on.
Arithmetic Pattern: The difference between consecutive multiples of 75 is always 75.
Examples on Multiples of 75
Simple Multiples:
- 75: 75×1=7575×1=75
- 150: 75×2=15075×2=150
- 225: 75×3=22575×3=225
Larger Multiples:
- 750: 75×10=75075×10=750
- 1500: 75×20=150075×20=1500
- 2250: 75×30=225075×30=2250
Real-Life Examples
Time: 4500 seconds in 75 minutes is a multiple of 75 because 75×60=450075×60=4500.
Money: $75 is a multiple of 75 because 75×1=7575×1=75.
Measurements: 75 feet is a multiple of 75 because 75×1=7575×1=75.
Practical Examples of Multiples of 75
- Time: An hour and 15 minutes equals 75 minutes, which is 75×1=7575×1=75.
- Money: A $150 bill can be paid using two $75 bills since 75×2=15075×2=150.
- Distance: A 225-mile road trip can be divided into three segments of 75 miles each because 75×3=22575×3=225.
- Weight: A shipment weighing 300 pounds can be split into four boxes of 75 pounds each, as 75×4=30075×4=300.
- Class Size: If a school has 375 students and they are split into five classes, each class would have 75 students because 75×5=37575×5=375.
Practical Applications
Counting by Seventy-Fives: When counting by seventy-fives (75, 150, 225, 300…), you are listing the multiples of 75.
Multiples of 75: Any number that is a multiple of 75, such as 300 or 375, can be divided evenly by 75.
Is 600 a multiple of 75?
Yes, 600 is a multiple of 75 because 75×8=600
Is 50 a multiple of 75?
No, 50 is not a multiple of 75 because it cannot be divided evenly by 75.
What is the 10th multiple of 75?
The 10th multiple of 75 is 750.
Are multiples of 75 also multiples of 5?
Yes, all multiples of 75 are also multiples of 5.
Is 1125 a multiple of 75?
Yes, 1125 is a multiple of 75 because 75×15=1125
What is the next multiple of 75 after 375?
The next multiple of 75 after 375 is 450.
Can multiples of 75 be negative?
Yes, multiples of 75 can be negative if 𝑛n is negative, such as -75, -150, and -225.
Is 0 a multiple of 75?
Yes, 0 is a multiple of 75 because 75×0=0
What are the multiples of 75 between 300 and 600?
The multiples of 75 between 300 and 600 are 375, 450, and 525.
Is 90 a multiple of 75?
No, 90 is not a multiple of 75 because it cannot be divided evenly by 75.
How do multiples of 75 help in real life?
Multiples of 75 are useful in various applications such as time management, financial calculations, and measurements.
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Practice Test
What is the fifth multiple of 75?
300
375
450
525
of 10
If 75 is multiplied by an odd number, which of the following could be the product?
225
300
375
450
of 10
What is the difference between the seventh and fourth multiples of 75?
150
225
300
375
of 10
Which of these numbers is not a multiple of 75?
600
675
725
750
of 10
What is the sum of the first three multiples of 75?
150
225
375
525
of 10
Which multiple of 75 is closest to 1000?
900
975
1050
1125
of 10
If a number is a multiple of 75, which of the following must it also be divisible by?
5
15
Both A and B
None of the above
of 10
Which of the following numbers is the greatest multiple of 75 less than 800?
675
750
825
900
of 10
What is the smallest multiple of 75 greater than 500?
525
575
600
675
of 10