Multiples of 60
Multiples of 60
Multiples of 60 are numbers that can be expressed as 60 times an integer. These numbers are also known as even numbers. Starting from 60, they follow a consistent pattern, increasing by 60 each time (e.g., 60, 120, 180, 240, 300, etc.). Multiples of 60 play a fundamental role in arithmetic and number theory, forming the basis for understanding even and odd numbers and serving as building blocks for more complex mathematical concepts. Recognizing and working with multiples of 60 is essential for performing various arithmetic operations efficiently.
What are Multiples of 60?
Multiples of 60 are numbers that can be expressed as 60×n, where n is an integer. These numbers are always even and include values like 60, 120, 180, 240, and so on.
Prime Factorization of 60:2 × 2 × 3 × 5
First 10 Multiples of 60 are 60, 120, 180, 240, 300, 360, 420, 480, 540, 600
First 50 Multiples of 60 are 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, 2160, 2220, 2280, 2340, 2400, 2460, 2520, 2580, 2640, 2700, 2760, 2820, 2880, 2940, 3000
For example, 60, 120, 180 and 240 are all multiples of 60, 88 is not a multiple of 60 for the following reasons:
| Number | Reason | Remainder |
|---|---|---|
| 60 | Multiple of 60 because 60 ÷ 60 = 1 | 0 |
| 120 | Multiple of 60 because 120 ÷ 60 = 2 | 0 |
| 180 | Multiple of 60 because 180 ÷ 60 = 3 | 0 |
| 240 | Multiple of 60 because 240 ÷ 60 = 4 | 0 |
| 88 | Not a multiple of 60 because 88 ÷ 60 = 1 with a remainder | 28 |
List of First 100 Multiples of 60 with Remainders
| Number | Reason | Remainder |
|---|---|---|
| 60 | Multiple of 60 because 60 ÷ 60 = 1 | 0 |
| 120 | Multiple of 60 because 120 ÷ 60 = 2 | 0 |
| 180 | Multiple of 60 because 180 ÷ 60 = 3 | 0 |
| 240 | Multiple of 60 because 240 ÷ 60 = 4 | 0 |
| 300 | Multiple of 60 because 300 ÷ 60 = 5 | 0 |
| 360 | Multiple of 60 because 360 ÷ 60 = 6 | 0 |
| 420 | Multiple of 60 because 420 ÷ 60 = 7 | 0 |
| 480 | Multiple of 60 because 480 ÷ 60 = 8 | 0 |
| 540 | Multiple of 60 because 540 ÷ 60 = 9 | 0 |
| 600 | Multiple of 60 because 600 ÷ 60 = 10 | 0 |
| 660 | Multiple of 60 because 660 ÷ 60 = 11 | 0 |
| 720 | Multiple of 60 because 720 ÷ 60 = 12 | 0 |
| 780 | Multiple of 60 because 780 ÷ 60 = 13 | 0 |
| 840 | Multiple of 60 because 840 ÷ 60 = 14 | 0 |
| 900 | Multiple of 60 because 900 ÷ 60 = 15 | 0 |
| 960 | Multiple of 60 because 960 ÷ 60 = 16 | 0 |
| 1020 | Multiple of 60 because 1020 ÷ 60 = 17 | 0 |
| 1080 | Multiple of 60 because 1080 ÷ 60 = 18 | 0 |
| 1140 | Multiple of 60 because 1140 ÷ 60 = 19 | 0 |
| 1200 | Multiple of 60 because 1200 ÷ 60 = 20 | 0 |
| 1260 | Multiple of 60 because 1260 ÷ 60 = 21 | 0 |
| 1320 | Multiple of 60 because 1320 ÷ 60 = 22 | 0 |
| 1380 | Multiple of 60 because 1380 ÷ 60 = 23 | 0 |
| 1440 | Multiple of 60 because 1440 ÷ 60 = 24 | 0 |
| 1500 | Multiple of 60 because 1500 ÷ 60 = 25 | 0 |
| 1560 | Multiple of 60 because 1560 ÷ 60 = 26 | 0 |
| 1620 | Multiple of 60 because 1620 ÷ 60 = 27 | 0 |
| 1680 | Multiple of 60 because 1680 ÷ 60 = 28 | 0 |
| 1740 | Multiple of 60 because 1740 ÷ 60 = 29 | 0 |
| 1800 | Multiple of 60 because 1800 ÷ 60 = 30 | 0 |
| 1860 | Multiple of 60 because 1860 ÷ 60 = 31 | 0 |
| 1920 | Multiple of 60 because 1920 ÷ 60 = 32 | 0 |
| 1980 | Multiple of 60 because 1980 ÷ 60 = 33 | 0 |
| 2040 | Multiple of 60 because 2040 ÷ 60 = 34 | 0 |
| 2100 | Multiple of 60 because 2100 ÷ 60 = 35 | 0 |
| 2160 | Multiple of 60 because 2160 ÷ 60 = 36 | 0 |
| 2220 | Multiple of 60 because 2220 ÷ 60 = 37 | 0 |
| 2280 | Multiple of 60 because 2280 ÷ 60 = 38 | 0 |
| 2340 | Multiple of 60 because 2340 ÷ 60 = 39 | 0 |
| 2400 | Multiple of 60 because 2400 ÷ 60 = 40 | 0 |
| 2460 | Multiple of 60 because 2460 ÷ 60 = 41 | 0 |
| 2520 | Multiple of 60 because 2520 ÷ 60 = 42 | 0 |
| 2580 | Multiple of 60 because 2580 ÷ 60 = 43 | 0 |
| 2640 | Multiple of 60 because 2640 ÷ 60 = 44 | 0 |
| 2700 | Multiple of 60 because 2700 ÷ 60 = 45 | 0 |
| 2760 | Multiple of 60 because 2760 ÷ 60 = 46 | 0 |
| 2820 | Multiple of 60 because 2820 ÷ 60 = 47 | 0 |
| 2880 | Multiple of 60 because 2880 ÷ 60 = 48 | 0 |
| 2940 | Multiple of 60 because 2940 ÷ 60 = 49 | 0 |
| 3000 | Multiple of 60 because 3000 ÷ 60 = 50 | 0 |
| 3060 | Multiple of 60 because 3060 ÷ 60 = 51 | 0 |
| 3120 | Multiple of 60 because 3120 ÷ 60 = 52 | 0 |
| 3180 | Multiple of 60 because 3180 ÷ 60 = 53 | 0 |
| 3240 | Multiple of 60 because 3240 ÷ 60 = 54 | 0 |
| 3300 | Multiple of 60 because 3300 ÷ 60 = 55 | 0 |
| 3360 | Multiple of 60 because 3360 ÷ 60 = 56 | 0 |
| 3420 | Multiple of 60 because 3420 ÷ 60 = 57 | 0 |
| 3480 | Multiple of 60 because 3480 ÷ 60 = 58 | 0 |
| 3540 | Multiple of 60 because 3540 ÷ 60 = 59 | 0 |
| 3600 | Multiple of 60 because 3600 ÷ 60 = 60 | 0 |
| 3660 | Multiple of 60 because 3660 ÷ 60 = 61 | 0 |
| 3720 | Multiple of 60 because 3720 ÷ 60 = 62 | 0 |
| 3780 | Multiple of 60 because 3780 ÷ 60 = 63 | 0 |
| 3840 | Multiple of 60 because 3840 ÷ 60 = 64 | 0 |
| 3900 | Multiple of 60 because 3900 ÷ 60 = 65 | 0 |
| 3960 | Multiple of 60 because 3960 ÷ 60 = 66 | 0 |
| 4020 | Multiple of 60 because 4020 ÷ 60 = 67 | 0 |
| 4080 | Multiple of 60 because 4080 ÷ 60 = 68 | 0 |
| 4140 | Multiple of 60 because 4140 ÷ 60 = 69 | 0 |
| 4200 | Multiple of 60 because 4200 ÷ 60 = 70 | 0 |
| 4260 | Multiple of 60 because 4260 ÷ 60 = 71 | 0 |
| 4320 | Multiple of 60 because 4320 ÷ 60 = 72 | 0 |
| 4380 | Multiple of 60 because 4380 ÷ 60 = 73 | 0 |
| 4440 | Multiple of 60 because 4440 ÷ 60 = 74 | 0 |
| 4500 | Multiple of 60 because 4500 ÷ 60 = 75 | 0 |
| 4560 | Multiple of 60 because 4560 ÷ 60 = 76 | 0 |
| 4620 | Multiple of 60 because 4620 ÷ 60 = 77 | 0 |
| 4680 | Multiple of 60 because 4680 ÷ 60 = 78 | 0 |
| 4740 | Multiple of 60 because 4740 ÷ 60 = 79 | 0 |
| 4800 | Multiple of 60 because 4800 ÷ 60 = 80 | 0 |
| 4860 | Multiple of 60 because 4860 ÷ 60 = 81 | 0 |
| 4920 | Multiple of 60 because 4920 ÷ 60 = 82 | 0 |
| 4980 | Multiple of 60 because 4980 ÷ 60 = 83 | 0 |
| 5040 | Multiple of 60 because 5040 ÷ 60 = 84 | 0 |
| 5100 | Multiple of 60 because 5100 ÷ 60 = 85 | 0 |
| 5160 | Multiple of 60 because 5160 ÷ 60 = 86 | 0 |
| 5220 | Multiple of 60 because 5220 ÷ 60 = 87 | 0 |
| 5280 | Multiple of 60 because 5280 ÷ 60 = 88 | 0 |
| 5340 | Multiple of 60 because 5340 ÷ 60 = 89 | 0 |
| 5400 | Multiple of 60 because 5400 ÷ 60 = 90 | 0 |
| 5460 | Multiple of 60 because 5460 ÷ 60 = 91 | 0 |
| 5520 | Multiple of 60 because 5520 ÷ 60 = 92 | 0 |
| 5580 | Multiple of 60 because 5580 ÷ 60 = 93 | 0 |
| 5640 | Multiple of 60 because 5640 ÷ 60 = 94 | 0 |
| 5700 | Multiple of 60 because 5700 ÷ 60 = 95 | 0 |
| 5760 | Multiple of 60 because 5760 ÷ 60 = 96 | 0 |
| 5820 | Multiple of 60 because 5820 ÷ 60 = 97 | 0 |
| 5880 | Multiple of 60 because 5880 ÷ 60 = 98 | 0 |
| 5940 | Multiple of 60 because 5940 ÷ 60 = 99 | 0 |
| 6000 | Multiple of 60 because 6000 ÷ 60 = 100 | 0 |
Read More About Multiples of 60
Important Notes
Even Numbers : All multiples of 60 are even numbers. This means they end in 0, 2, 4, 6, or 8.
Divisibility : A number is a multiple of 60 if it can be divided by 60 with no remainder.
Factors : Multiples of 60 have 60 as one of their factors. Additionally, they also have 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 as factors since these are the factors of 60.
Infinite Sequence : There are infinitely many multiples of 60, extending indefinitely as 60, 120, 180, 240, 300, and so on.
Arithmetic Pattern : The difference between consecutive multiples of 60 is always 60.
Examples on Multiples of 60
Simple Multiples:
- 60: 60 × 1 = 60
- 120: 60 × 2 = 120
- 180: 60 × 3 = 180
Larger Multiples:
- 300: 60 × 5 = 300
- 600: 60 × 10 = 600
- 1200: 60 × 20 = 1200
Very Large Multiples:
- 3000: 60 × 50 = 3000
- 6000: 60 × 100 = 6000
- 12000: 60 × 200 = 12000
Real-Life Examples
Time:
60 seconds in a minute: This is a multiple of 60 because 60 × 1 = 60.
Money:
- $60: This is a multiple of 60 because 60 × 1 = 60. (For example, 6 ten-dollar bills)
Measurements:
- 60 inches: This is a multiple of 60 because 60 × 1 = 60. (For example, 5 feet, as each foot is 12 inches)
Cycles and Periods:
- 60 minutes in an hour: This is a multiple of 60 because 60 × 1 = 60.
Angles:
- 60 degrees: An angle of 60 degrees is a multiple of 60 because 60 × 1 = 60. This is one of the angles in an equilateral triangle.
Practical Examples of Multiples of 60
If a recipe requires you to bake a cake for 180 minutes, how many hours do you need to bake it?
180 minutes is a multiple of 60 (180 ÷ 60 = 3). You need to bake the cake for 3 hours.
You are planning a road trip, and you know that you travel 60 miles every hour. How far will you have traveled after 5 hours?
60 miles per hour multiplied by 5 hours is 60 × 5 = 300 miles. You will have traveled 300 miles.
You are doing a workout routine that includes 60 push-ups in total. If you do sets of 15 push-ups each, how many sets do you need to complete?
60 push-ups divided by 15 push-ups per set is 60 ÷ 15 = 4 sets. You need to complete 4 sets.
A movie marathon lasts for 360 minutes. How many hours is the marathon?
360 minutes is a multiple of 60 (360 ÷ 60 = 6). The movie marathon lasts for 6 hours.
Practical Applications
Counting by Sixties: When counting by sixties (60, 120, 180, 240…), you are listing the multiples of 60.
Time Measurement: Any multiple of 60, such as 120 minutes or 360 seconds, represents a common time measurement because they are evenly divisible by 60.
Monetary Calculation: Any monetary value that is a multiple of 60, such as $180 or $300, can be easily divided into smaller units of $60.
Can a negative number be a multiple of 60?
Yes, negative numbers can be multiples of 60, such as -60, -120, -180, etc.
Is 100 a multiple of 60?
No, 100 is not a multiple of 60 because 100 ÷ 60 = 1.6667, which is not an integer.
What is the sum of the first three multiples of 60?
The sum of the first three multiples of 60 is 60 + 120 + 180 = 360.
Are multiples of 60 divisible by 12?
Yes, multiples of 60 are divisible by 12 because 60 is a multiple of 12.
How many multiples of 60 are there between 1 and 1000?
There are 16 multiples of 60 between 1 and 1000 (60 × 1 to 60 × 16).
Is 720 a multiple of 60?
Yes, 720 is a multiple of 60 because 720 ÷ 60 = 12.
What is the greatest multiple of 60 less than 500?
The greatest multiple of 60 less than 500 is 480 (60 × 8 = 480).
How do multiples of 60 relate to time?
Multiples of 60 are used in time measurements, such as seconds in a minute and minutes in an hour.
What is the least common multiple (LCM) of 60 and 90?
The least common multiple of 60 and 90 is 180.
Can multiples of 60 be prime numbers?
No, multiples of 60 cannot be prime numbers because they have more than two factors.
What is the product of the first two multiples of 60?
The product of the first two multiples of 60 is 60 × 120 = 7200.
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