# Factors of 420

So you need to find the factors of 420 do you? In this quick guide we'll describe what the factors of 420 are, how you find them and list out the factor pairs of 420 for you to prove the calculation works. Let's dive in!

## Factors of 420 Definition

When we talk about the factors of 420, what we really mean is all of the positive and negative integers (whole numbers) that can be evenly divided into 420. If you were to take 420 and divide it by one of its factors, the answer would be another factor of 420.

Let's look at how to find all of the factors of 420 and list them out.

## How to Find the Factors of 420

We just said that a factor is a number that can be divided equally into 420. So the way you find and list all of the factors of 420 is to go through every number up to and including 420 and check which numbers result in an even quotient (which means no decimal place).

Doing this by hand for large numbers can be time consuming, but it's relatively easy for a computer program to do it. Our calculator has worked this out for you. Here are all of the factors of 420:

• 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 ÷ 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

All of these factors can be used to divide 420 by and get a whole number. The full list of positive factors for 420 are:

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

## Negative Factors of 420

Technically, in math you can also have negative factors of 420. If you are looking to calculate the factors of a number for homework or a test, most often the teacher or exam will be looking for specifically positive numbers.

However, we can just flip the positive numbers into negatives and those negative numbers would also be factors of 420:

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

## How Many Factors of 420 Are There?

As we can see from the calculations above there are a total of 24 positive factors for 420 and 24 negative factors for 420 for a total of 48 factors for the number 420.

There are 24 positive factors of 420 and 24 negative factors of 420. Wht are there negative numbers that can be a factor of 420?

## Factor Pairs of 420

A factor pair is a combination of two factors which can be multiplied together to equal 420. For 420, all of the possible factor pairs are listed below:

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

Just like before, we can also list out all of the negative factor pairs for 420:

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

Notice in the negative factor pairs that because we are multiplying a minus with a minus, the result is a positive number.

So there you have it. A complete guide to the factors of 420. You should now have the knowledge and skills to go out and calculate your own factors and factor pairs for any number you like.

Feel free to try the calculator below to check another number or, if you're feeling fancy, grab a pencil and paper and try and do it by hand. Just make sure to pick small numbers!

## Factors Calculator

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Factors of 421