# What are all the factors, the prime factorization, and factor pairs of 420?

To find the factors of 420, divide 420 by each number starting with 1 and working up to 420

## What is a factor in math ?

Factors are the numbers you multiply together to get another number. For example, the factors of 15 are 3 and 5 because 3 × 5 = 15.

The factors of a number can be positive or negative, but they cannot be zero.

The factors of a number can be used to find out if the number is prime or not.

A prime number is a number that has only two factors: itself and 1. For example, the number 7 is prime because its only factors are 7 and 1.

## List all of the factors of 420 ?

To calculate the factors of 420 , you can use the division method.

1. Begin by dividing 420 by the smallest possible number, which is 2.

2. If the division is even, then 2 is a factor of 420.

3. Continue dividing 420 by larger numbers until you find an odd number that does not divide evenly into 420 .

4. The numbers that divide evenly into 420 are the factors of 420 .

Now let us find how to calculate all the factors of Four hundred twenty :

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

As you can see, the factors of 420 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 20 , 21 , 28 , 30 , 35 , 42 , 60 , 70 , 84 , 105 , 140 , 210 and 420 .

## How many factors of 420 are there ?

The factors of 420 are the numbers that can evenly divide 420 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 20 , 21 , 28 , 30 , 35 , 42 , 60 , 70 , 84 , 105 , 140 , 210 and 420.

Thus, there are a total of 25 factors of 420

## What are the factor pairs of 420 ?

Factor Pairs of 420 are combinations of two factors that when multiplied together equal 420. There are many ways to calculate the factor pairs of 420 .

One easy way is to list out the factors of 420 :
1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 20 , 21 , 28 , 30 , 35 , 42 , 60 , 70 , 84 , 105 , 140 , 210 , 420

Then, pair up the factors:
(1,420),(2,210),(3,140),(4,105),(5,84),(6,70),(7,60),(10,42),(12,35),(14,30),(15,28) and (20,21) These are the factor pairs of 420 .

## Prime Factorisation of 420

There are a few different methods that can be used to calculate the prime factorization of a number. Two of the most common methods are listed below.

1) Use a factor tree :

1. Take the number you want to find the prime factorization of and write it at the top of the page

2. Find the smallest number that goes into the number you are finding the prime factorization of evenly and write it next to the number you are finding the prime factorization of

3. Draw a line under the number you just wrote and the number you are finding the prime factorization of

4. Repeat step 2 with the number you just wrote until that number can no longer be divided evenly

5. The numbers written on the lines will be the prime factors of the number you started with

For example, to calculate the prime factorization of 420 using a factor tree, we would start by writing 420 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 420 would be 2 x 2 x 3 x 5 x 7.

2) Use a factorization method :

There are a few different factorization methods that can be used to calculate the prime factorization of a number.

One common method is to start by dividing the number by the smallest prime number that will divide evenly into it.

Then, continue dividing the number by successively larger prime numbers until the number has been fully factorised.

For example, to calculate the prime factorization of 420 using this method, we keep dividing until it gives a non-zero remainder.

420 ÷ 2 = 210
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So the prime factors of 420 are 2 x 2 x 3 x 5 x 7.

## Frequently Asked Questions on Factors

### What are all the factors of 420 ?

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

### What is the prime factorization of 420 ?

The prime factorization of 420 is 2 x 2 x 3 x 5 x 7 or 22 x 31 x 51 x 71, where 2 , 3 , 5 , 7 are the prime numbers .

### What are the prime factors of 420 ?

The prime factors of 420 are 2 , 3 , 5 , 7 .

### Is 420 a prime number ?

A prime number is a number that has only two factors 1 and itself.
420 it is not a prime number because it has the factors 1 , 2 , 3 , 4 , 5 , 6 , 7 , 10 , 12 , 14 , 15 , 20 , 20 , 21 , 28 , 30 , 35 , 42 , 60 , 70 , 84 , 105 , 140 , 210 and 420.