# All factors of 420

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How many factors does 420 have?

24 numbers will factor into 420. This means that there are 24 numbers 420 can be divided by completely, with no remainder.

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The factors of 420 include:

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420.

#### The factors of 420 in pairs include:

1 - 420,

2 -210

3-140

4-105

8-84

6-70

7-60

10-42

12-35

14-30

15-28

20-21

Remember that a prime number is a number greater than 1 that can only be evenly divided by itself and 1. For example, 5 is a prime number.

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**Is 420 a prime number?**

No, because it can be evenly divided by numbers other than itself and 1.

A composite number can be divided by numbers other than itself and 1 exactly (no remainder). To put it another way, numbers besides 1 and the number itself can be multiplied together to equal that number.

**Is 420 composite?**

Yes, 420 is composite because many numbers besides 420 and 1 can be multiplied together to equal 420 (i.e. 2 and3, etc.). 420 can be divided by numbers like 2, and 3 with no remainder.

What is the prime factorization of a number? The prime factorization of a number is the process of finding all the prime factors that multiply together to equal a given number.

For instance, the prime factorization of 12 is 2 x 2 x 3 = 12.

How can we find the prime factorization of 420?

I like to create a factor tree.

See the picture below for a factor tree of 420.

**Prime factorization of 420 **

2 x 2 x 3 x 5 x7 = 420

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