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.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60 ...

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 n^th Multiple of 4

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

Example:

Find the 50^th multiple of 4.

The n^th multiple of 4 is 4n.

The 50^th 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.

Facts About 4

• 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.

Check What I Know?

Question 1Recognize multiples of 4

What are the first five positive multiples of 4?

Answer

4, 8, 12, 16, 20.

They are found by multiplying 4 by 1, 2, 3, 4, and 5.

Question 2Continue the sequence

What comes after 20 in the sequence of positive multiples of 4?

Answer

24.

Add 4 to 20.

Question 3Check a multiple

Is 32 a multiple of 4?

Answer

Yes. 32 = 4 × 8.

A number is a multiple when it is the product of the original number and an integer.

Question 4Use division to verify

How can division confirm that 36 is a multiple of 4?

Answer

36 ÷ 4 = 9, with no remainder.

A whole-number quotient confirms the multiple.

Question 5Review: Finding the multiples of 4 by skip counting

What key idea does the article explain about “Finding the multiples of 4 by skip counting”?

Answer

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

Question 6Review: Find the multiples of 4 by multiplication

What key idea does the article explain about “Find the multiples of 4 by multiplication”?

Answer

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.

Question 7Review: The nth Multiple of 4

What key idea does the article explain about “The nth Multiple of 4”?

Answer

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 $$4 \times 50 = 200$$