Multiples of 107

Multiples of 107 are the products of 107 and any integer. In mathematics, a multiple is a number that can be divided by another number without a remainder. When you multiply 107 by an integer, you get a multiple of 107. For instance, 214 is a multiple of 107 because 107 × 2 = 214. Understanding multiples is fundamental in number theory, as it helps in identifying factors and divisors.

For example, 321, 535, 749 and 963 are all multiples of 107, 975 is not a multiple of 107 for the following reasons:

List of First 100 Multiples of 107 with Remainders

Read More About Multiples of 107

Table of 107

Important Notes

Definition of Multiples:

• A multiple of 107 is any number that can be expressed as 107 times an integer.
• Formally, if n is an integer, then 107×n is a multiple of 107.

Sequence of Multiples:

• The sequence starts with 107 and increases by 107 for each subsequent multiple.
• The first few multiples of 107 are: 107, 214, 321, 428, 535, etc.

Characteristics:

• Multiples of 107 are always positive if the integer multiplier is positive and negative if the integer multiplier is negative.
• Each multiple of 107 is 107 units apart from the next multiple.

Divisibility:

• A number is a multiple of 107 if and only if it can be divided by 107 without leaving a remainder.
• For example, 2140 divided by 107 equals 20, which is an integer, so 2140 is a multiple of 107.

Practical Uses:

• Understanding multiples of 107 is useful in problems involving division, factorization, and least common multiples.
• They also appear in patterns, sequences, and in solving algebraic equations where 107 is a factor.

Examples on Multiples of 107

First Ten Multiples of 107:

• 107 × 1 = 107
• 107 × 2 = 214
• 107 × 3 = 321
• 107 × 4 = 428
• 107 × 5 = 535
• 107 × 6 = 642
• 107 × 7 = 749
• 107 × 8 = 856
• 107 × 9 = 963
• 107 × 10 = 1070

Properties and Patterns:

Additive Property: The sum of two multiples of 107 is also a multiple of 107.

Example: 214 + 428 = 642 (both 214 and 428 are multiples of 107, and so is 642).

Subtracting Property: The difference between two multiples of 107 is also a multiple of 107.

Example: 856 – 535 = 321 (both 856 and 535 are multiples of 107, and so is 321).

Real-world Applications:

Scheduling: If an event occurs every 107 days, the schedule can be determined using multiples of 107.

Example: If an event starts on January 1st, the next occurrence will be on April 18th (107 days later), then on August 3rd (214 days later), and so on.

Bulk Quantities: In manufacturing, ordering parts in multiples of 107 can help in inventory management.

Example: If a factory orders screws in batches of 107, ordering 5 batches means they receive 535 screws (5 × 107).

Large Multiples:

• 107 × 20 = 2140
• 107 × 50 = 5350
• 107 × 100 = 10700
• 107 × 500 = 53500

Practical Example in Measurements:

Distance: If a car travels 107 miles in one trip, then over multiple trips, the distance covered can be calculated using multiples of 107.

Example: Over 3 trips, the car travels 321 miles (107 × 3 = 321).

Summary Table of First 20 Multiples of 107

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