# Multiples of 107

Created by: Team Maths - Examples.com, Last Updated: August 22, 2024

## 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.

## What are Multiples of 107?

Multiples of 107 are the numbers obtained by multiplying 107 with any integer. These multiples can be expressed as 107n, where n is an integer. They are important in understanding patterns and relationships in number theory.

Prime Factorization of 107: 107 First 10 Multiples of 107 are 107, 214, 321, 428, 535, 642, 749, 856, 963, 1070.

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).

## What are multiples of 107?

Multiples of 107 are numbers that can be evenly divided by 107 without leaving a remainder.

## How do I find the multiples of 107?

Simply multiply 107 by integers (whole numbers) starting from 1: 107, 214, 321, 428, and so on.

## Are there any patterns in the multiples of 107?

Yes, if you look closely, you’ll notice that the units digit of multiples of 107 repeats every 4th multiple. This is because 107 ends in 7, and the cycle of units digits for powers of 7 is 7, 9, 3, 1.

## Do multiples of 107 have any special properties?

Multiples of 107 are odd numbers because 107 is an odd number itself. Also, every multiple of 107 is 107 times some integer.

## Can multiples of 107 be negative?

Yes, multiples of 107 can be negative if you multiply 107 by negative integers. For example, -107, -214, -321, and so on.

## How do multiples of 107 relate to prime numbers?

107 itself is a prime number, so its multiples are only divisible by 1 and themselves. Therefore, the multiples of 107 are not divisible by any other prime number except 107.

## Are there any real-life applications of multiples of 107?

In finance or accounting, multiples of 107 could be used in calculations involving interest rates or investments.

## What is the significance of the 107th multiple?

The 107th multiple of 107 is 11,449. It doesn’t have any particular mathematical significance, but it’s interesting to note.

## Can multiples of 107 form a sequence?

Yes, the multiples of 107 form an arithmetic sequence with a common difference of 107.

## Are there any famous mathematical problems related to multiples of 107?

Not specifically related to 107, but multiples and divisibility are fundamental concepts in number theory and have connections to many famous mathematical problems like the Goldbach conjecture or the Twin Prime conjecture.

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