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.

## 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 x 4 = 4
- Second multiple: 2 x 4 = 4
- Third multiple: 3 x 4 = 12
- Fourth multiple: 4 x 4 = 16
- Fifth multiple: 5 x 4 = 20

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

## The nth Multiple of 4

The *n ^{th}* multiple of 4 is given by

*4n*. That is, to find the multiple in the

*n*place of the multiples sequence, we multiply

^{th}*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 x 50 = 200**

## The Factors and Multiples of 4

- The factors of 4 are the values the give the product 4 when multiplied.1 x 4 = 4; 2 x 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

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:

- 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?

Write the first 10 multiples of 4 using skip counting.

The first 10 multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.

The skip counting is done by adding 4 repeatedly.

Number | Add 4 to the previous value | Multiple |

1 | 4 | 4 |

2 | 4+4 | 8 |

3 | 8+4 | 12 |

4 | 12+4 | 16 |

5 | 16+4 | 20 |

6 | 20+4 | 24 |

7 | 24+4 | 28 |

8 | 28+4 | 32 |

9 | 32+4 | 36 |

10 | 36+4 | 40 |

Write down all the multiples of 4 between 100 and 130.

all the multiples we have got *104, 108, 112, 116, 120, 124, 128*

To find the next multiple after 100, check if 100 is divisible by 4.

Since 100 is divisible by 4, we can find the next multiple by adding 4 to 100.

100+4=104

104+4=108

108+4=112

112+4=116

116+4=120

120+4=124

124+4=128

We cannot add further because the value will exceed 130.

Peggy is out at the apple farm to pluck some apples to see if they are ready to store. She decides to take an apple from every 4^{th} tree. In the end, she has 68 apples in the basket. What is the least number of trees on the farm if Peggy has taken an apple from every 4^{ th} tree?

*There are at least 272 trees on the farm.*

If Peggy has taken one apple from every 4^{ th} tree, then she must have moved 68 groups of 4^{th} trees.

68 groups of 4 trees are 68×4=272

Find the least common multiples of 4, 8 and 16.

The least common multiple of 4, 8 and 16 is 16.

The multiples of 4 are 4, 8, 12, **16**, 20, 24

The multiples of 8 are 8, **16**, 24, 32, 40

The multiples of 16 are **16**, 32, 48, 64, 80

The multiple that is common to all the three numbers is 16.

Jim is making sandwiches for the picnic. He is cutting one sandwich into 4 bite-size pieces. If he has planned to make 60 such pieces, what is the number of slices of bread he needs to make it?

Jim needs 30 slices of bread

Jim needs 60 pieces of sandwiches

If 4 pieces are made from 1 sandwich, the number of sandwiches required to make 60 pieces would be

Hence Jim needs 15 sandwiches.

Each sandwich is made of 2 slices of bread.

The number of slices required to make 15 sandwiches is

Find the 75^{ th} multiple of 4 and add it to the next two consecutive multiples of 4.

The required answer is 912.

The **n ^{th}** multiple of

**4**is given by

**4n**.

The **75th** multiple of **4** is

The next consecutive multiple is found by adding **4** to **300**

300+4 = 304

304+4=308

Now add 300 to its next two consecutive multiples

300+304+308= 912

Three bells in a church ring once every 2 minutes, 4 minutes, and 6 minutes respectively. If the bells rang together now, after how many minutes will they ring together again?

Let us list down the minutes in which each of the 3 bells ring.

Number | I^{st} bell | 2^{nd} bell | 3^{rd} bell |

1 | 2 minutes | 4 minutes | 6 minutes |

2 | 4 minutes | 8 minutes | 12 minutes |

3 | 6 minutes | 12 minutes | 18 minutes |

4 | 8 minutes | 16 minutes | 24 minutes |

5 | 10 minutes | 20 minutes | 30 minutes |

6 | 12 minutes | 24 minutes | 36 minutes |

We can see that the first time that the 3 bells ring together is after 12 minutes.

## Frequently Asked Questions

The composite number is the number that has factors other than 1 and the number itself. The numbers before 4 are 1, 2 and 3. 1 is neither prime nor composite, 2 and 3 are prime numbers. Hence 4 is the first number to have 2 also as a factor and hence is the first composite number.

The easiest method is to see if the number is even or odd. Because all the multiples of 4 are even.

If the number is even, observe the last to digits of the number. If they are either 00 or divisible by 4, then the number is divisible by 4.

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