# What are all the factors, the prime factorization, and factor pairs of 840?

To find the factors of 840, divide 840 by each number starting with 1 and working up to 840

## 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 840 ?

To calculate the factors of 840 , you can use the division method.

1. Begin by dividing 840 by the smallest possible number, which is 2.

2. If the division is even, then 2 is a factor of 840.

3. Continue dividing 840 by larger numbers until you find an odd number that does not divide evenly into 840 .

4. The numbers that divide evenly into 840 are the factors of 840 .

Now let us find how to calculate all the factors of Eight hundred forty :

840 ÷ 1 = 840
840 ÷ 2 = 420
840 ÷ 3 = 280
840 ÷ 4 = 210
840 ÷ 5 = 168
840 ÷ 6 = 140
840 ÷ 7 = 120
840 ÷ 8 = 105
840 ÷ 10 = 84
840 ÷ 12 = 70
840 ÷ 14 = 60
840 ÷ 15 = 56
840 ÷ 20 = 42
840 ÷ 21 = 40
840 ÷ 24 = 35
840 ÷ 28 = 30
840 ÷ 30 = 28
840 ÷ 35 = 24
840 ÷ 40 = 21
840 ÷ 42 = 20
840 ÷ 56 = 15
840 ÷ 60 = 14
840 ÷ 70 = 12
840 ÷ 84 = 10
840 ÷ 105 = 8
840 ÷ 120 = 7
840 ÷ 140 = 6
840 ÷ 168 = 5
840 ÷ 210 = 4
840 ÷ 280 = 3
840 ÷ 420 = 2
840 ÷ 840 = 1

As you can see, the factors of 840 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 10 , 12 , 14 , 15 , 20 , 21 , 24 , 28 , 30 , 35 , 40 , 42 , 56 , 60 , 70 , 84 , 105 , 120 , 140 , 168 , 210 , 280 , 420 and 840 .

## How many factors of 840 are there ?

The factors of 840 are the numbers that can evenly divide 840 . These numbers are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 10 , 12 , 14 , 15 , 20 , 21 , 24 , 28 , 30 , 35 , 40 , 42 , 56 , 60 , 70 , 84 , 105 , 120 , 140 , 168 , 210 , 280 , 420 and 840.

Thus, there are a total of 32 factors of 840

## What are the factor pairs of 840 ?

Factor Pairs of 840 are combinations of two factors that when multiplied together equal 840. There are many ways to calculate the factor pairs of 840 .

One easy way is to list out the factors of 840 :
1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 10 , 12 , 14 , 15 , 20 , 21 , 24 , 28 , 30 , 35 , 40 , 42 , 56 , 60 , 70 , 84 , 105 , 120 , 140 , 168 , 210 , 280 , 420 , 840

Then, pair up the factors:
(1,840),(2,420),(3,280),(4,210),(5,168),(6,140),(7,120),(8,105),(10,84),(12,70),(14,60),(15,56),(20,42),(21,40),(24,35) and (28,30) These are the factor pairs of 840 .

## Prime Factorisation of 840

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 840 using a factor tree, we would start by writing 840 on a piece of paper. Then, we would draw a line under it and begin finding factors.

The final prime factorization of 840 would be 2 x 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 840 using this method, we keep dividing until it gives a non-zero remainder.

840 ÷ 2 = 420
420 ÷ 2 = 210
210 ÷ 2 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So the prime factors of 840 are 2 x 2 x 2 x 3 x 5 x 7.

## Frequently Asked Questions on Factors

### What are all the factors of 840 ?

The factors of 840 are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 10 , 12 , 14 , 15 , 20 , 21 , 24 , 28 , 30 , 35 , 40 , 42 , 56 , 60 , 70 , 84 , 105 , 120 , 140 , 168 , 210 , 280 , 420 and 840.

### What is the prime factorization of 840 ?

The prime factorization of 840 is 2 x 2 x 2 x 3 x 5 x 7 or 23 x 31 x 51 x 71, where 2 , 3 , 5 , 7 are the prime numbers .

### What are the prime factors of 840 ?

The prime factors of 840 are 2 , 3 , 5 , 7 .

### Is 840 a prime number ?

A prime number is a number that has only two factors 1 and itself.
840 it is not a prime number because it has the factors 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 10 , 12 , 14 , 15 , 20 , 21 , 24 , 28 , 30 , 35 , 40 , 42 , 56 , 60 , 70 , 84 , 105 , 120 , 140 , 168 , 210 , 280 , 420 and 840.