# Multiples of 31

Created by: Team Maths - Examples.com, Last Updated: August 21, 2024

## Multiples of 31

Multiples of 31 are integers obtained by multiplying 31 with other whole numbers. In mathematics, a multiple of 31 can be represented as $31n$, where $n$ is an integer. This process involves multiplication, producing numbers like 31, 62, 93, and so on. Factors and divisors of these multiples include both 31 and the integer used in the multiplication. Understanding multiples of 31 helps in various mathematical problems involving divisibility and common factors.

## What are Multiples of 31?

Multiples of 31 are the products obtained by multiplying 31 by any integer. Examples include 31, 62, 93, 124, and so on. These numbers follow the pattern 31n, where n is any integer.

Prime Factorization of 31: 31¹ First 10 Multiples of 31 are 31, 62, 93, 124, 155, 186, 217, 248, 279, 310.

Table of 31

## Important Notes

### Definition:

• Multiples of 31 are numbers that can be expressed as 31 times an integer. Mathematically, a multiple of 31 is in the form 31×n, where n is an integer.

### Sequence:

• The sequence of multiples of 31 starts at 31 and increases by 31 with each subsequent multiple: 31, 62, 93, 124, 155, 186, etc.

### Divisibility Rule:

• A number is a multiple of 31 if, after dividing it by 31, the result is an integer without any remainder. For example, 155 is a multiple of 31 because 155÷31 = 5, which is an integer.

### Properties:

Multiples of 31 share certain properties:

• They are evenly spaced on the number line, with a constant difference of 31 between consecutive multiples.
• Every multiple of 31 is also a multiple of 1, 31, and their divisors (if any).

### Applications:

• Multiples of 31 can be useful in various mathematical and practical contexts, such as finding common multiples in problem-solving, understanding patterns in number theory, and solving equations that involve factors of 31.

## Examples on Multiples of 31

• 31×1 = 31
• 31×2 = 62
• 31×3 = 93

• 1×20 = 620
• 1×50 = 1550
• 31×100 = 310

### Real-Life Examples

• Days in a month: Most months have 30 or 31 days. For example, January has 31 days which is a multiple of 31 (31×1).
• Calendar years: 1860 is a multiple of 31 (31×60 = 1860).

## Practical Examples of Multiples of 31

### What is the 15th multiple of 31?

The 15th multiple of 31 is 31×15 = 465.

### Is 248 a multiple of 31?

No, 248 is not a multiple of 31 because it cannot be expressed as 31×n.

### What is the next multiple of 31 after 62?

The next multiple of 31 after 62 is 62+31 = 93.

### Find the 25th multiple of 31.

The 25th multiple of 31 is 31×25 = 775.

### Is 961 a multiple of 31?

Yes, 961 is a multiple of 31 because 31×31 = 961.

## What is a multiple of 31?

A multiple of 31 is any number that can be expressed as 31 times an integer. For example, 31, 62, 93, etc.

## How do you determine if a number is a multiple of 31?

To determine if a number is a multiple of 31, divide the number by 31. If the quotient is an integer with no remainder, the number is a multiple of 31.

## What is the smallest positive multiple of 31?

The smallest positive multiple of 31 is 31 itself (31×1 = 31).

## What are the first five multiples of 31?

The first five multiples of 31 are 31, 62, 93, 124, and 155.

## Is 465 a multiple of 31?

Yes, 465 is a multiple of 31 because 465 ÷ 31 = 15, which is an integer (31×15 = 465).

## What is the 10th multiple of 31?

The 10th multiple of 31 is 31×10 = 310.

## How can multiples of 31 be used in real life?

Multiples of 31 can be used in various contexts such as scheduling events (every 31 days), batch processing in manufacturing, or organizing data sets.

## What is the sum of the first three multiples of 31?

The sum of the first three multiples of 31 is 31 + 62 + 93 = 186.

## Can multiples of 31 be negative?

Yes, multiples of 31 can be negative. For example, -31, -62, and -93 are all multiples of 31.

## What is the largest multiple of 31 under 1000?

The largest multiple of 31 under 1000 is 31×32 = 992, as 31×33 = 1023 which is greater than 1000.

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