# What are the Multiples of 4?

The multiples of 4 are the values that we get by multiplying 4 to any number. The number 4 is the first multiple of itself.

The multiples of 4 begin with 4 and continue infinitely.

We can find the multiples of 4 by skip counting by 4’s or by multiplying any number with 4.

## Finding the multiples of 4 by skip counting

• First multiple: 4
• Second multiple: 4 + 4 = 8
• Third multiple: 8 + 4 = 12
• Fourth multiple: 12 + 4 = 16
• Fifth multiple: 16 + 4 = 20

The skip counting helps to find the multiples of 4 only to a certain point as we need to work out the multiples from the beginning each time.

## Find the multiples of 4 by multiplication

• First multiple: $$1\times 4 = 4$$
• Second multiple: $$2\times4 = 4$$
• Third multiple: $$3\times 4 = 12$$
• Fourth multiple: $$4\times 4 = 16$$
• Fifth multiple: $$5\times4 = 20$$

Using the multiplication method, the value of any number of multiples can be found out.

## The nth Multiple of 4

The nth multiple of 4 is given by 4n. That is, to find the multiple in the nth place of the multiples sequence, we multiply 4 to n.

Example:

Find the 50th multiple of 4.

The nth multiple of 4 is 4n.

The 50th multiple of 4 is $$4 \times 50 = 200$$

## The Factors and Multiples of 4

• The factors of 4 are the values the give the product 4 when multiplied. $$1 \times34 = 4$$;  $$2 \times3 2 = 4$$. The factors of 4 are 1, 2, and 4.
• The factors of 4 are different from the multiples of 4 as the factors are the values that are multiplied to get 4 whereas the multiples of 4 are the values obtained by multiplying 4 to any given number.
• The factors of 4 are different from the multiples of 4 as the factors are the values that are multiplied to get 4 whereas the multiples of 4 are the values obtained by multiplying 4 to any given number.
• All numbers are both factors and multiples of itself.

## Test of Divisibility for 4

The divisibility test for 4 helps to find if a number is divisible by 4.

If the last two digits of a number (the digits in the ten’s and one’s places) are divisible by 4, then the number is also divisible by 4.

Example:
Use the test of divisibility to find if the given number is divisible by 4.

516

Solution:
Consider the digits in the ten’s and the one’s place of the number. Here we have 16 as the last two digits.

Since 16 is a multiple of 4, the number 516 is also divisible by 4.

## The Least Common Multiples

We already know that multiples are values obtained by multiplying various numbers to a given number.

A common multiple is a value that is common to two numbers.

A least common multiple is the first value that is common to two numbers.

Example:

Find the least common multiple of 4 and 6.

Solution:
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32

The multiples of 6 are 6, 12, 18, 24, 30, 36

Here 12 is the multiple that is common to both 4 and 6. We can see that 24 is also a common multiple, but the multiple that occurs the first is called the least common multiple of the given numbers.

• The number 4 is the first number in the whole numbers to have prime factors other than 1 and itself. The factors of 4 are 1, 2 and 4. Here 2 is a prime factor.
• The number 4 is the first prime square number:
$$2^{2\;}=\;4\\$$
• The number 4 is the first composite even number.
• The value 0 is also a multiple of all the numbers as all the numbers multiplied by 0 gives 0.

## Did You Know?

The number 4 can divide all the numbers that have 00 as their last two
digits like 100, 2400, 8600, 1000, 10000, etc.

This is because 4 has 100 as its multiple. Since 100 is a multiple of 4 and is divisible by 4. All the numbers that have 00 as their last two digits are also divisible by 4 and are a multiple for 4.