# Factors of 20

Factors of 20 are 1, 2, 4, 5, 10, and 20

#### How to find factors of a number

 1.   Find factors of 20 using Division Method 2.   Find factors of 20 using Prime Factorization 3.   Find factors of 20 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 20

• Divide 20 by 1: 20 ÷ 1 : Remainder = 0
• Divide 20 by 2: 20 ÷ 2 : Remainder = 0
• Divide 20 by 4: 20 ÷ 4 : Remainder = 0
• Divide 20 by 5: 20 ÷ 5 : Remainder = 0
• Divide 20 by 10: 20 ÷ 10 : Remainder = 0
• Divide 20 by 20: 20 ÷ 20 : Remainder = 0

Hence, Factors of 20 are 1, 2, 4, 5, 10, and 20

#### 2. Steps to find factors of 20 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 20 using the division method, follow these steps:

• Step 1. Start dividing 20 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 20, which is 2. Divide 20 by 2 to obtain the quotient (10).
20 ÷ 2 = 10
• Step 3. Repeat step 1 with the obtained quotient (10).
10 ÷ 2 = 5
5 ÷ 5 = 1

So, the prime factorization of 20 is, 20 = 2 x 2 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 20 as shown below:

So, the prime factorization of 20 is, 20 = 2 x 2 x 5.

#### 3. Find factors of 20 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 20 would be the two numbers which, when multiplied, give 20 as the result.

The following table represents the calculation of factors of 20 in pairs:

Factor Pair Pair Factorization
1 and 20 1 x 20 = 20
2 and 10 2 x 10 = 20
4 and 5 4 x 5 = 20

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 20. They are called negative pair factors.

Hence, the negative pairs of 20 would be ( -1 , -20 ) , ( -2 , -10 ) and ( -4 , -5 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 20 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 20.
• Every number is a factor of zero (0), since 20 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 10, 20 are exact divisors of 20.
• Factors of 20 are 1, 2, 4, 5, 10, 20. Each factor divides 20 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 20 are all less than or equal to 20.

• What two numbers make 20?

Two numbers that make 20 are 2 and 10.

• What is prime factorization of 20?

Prime factorization of 20 is 2 x 2 x 5.

• Write some multiples of 20?

First five multiples of 20 are 40, 60, 80, 100.

• Which is the smallest prime factor of 20?

The smallest prime factor of 20 is 2.

• Is 20 a perfect square?

No 20 is not a perfect square.

• What is the sum of all factors of 20?

The sum of all factors of 20 is 42.

• What are factors of 20?

Factors of 20 are 1, 2, 4, 5, 10, 20.

• How do you find factors of a negative number? ( eg. -20 )?

Factors of -20 are -1, -2, -4, -5, -10, -20.

• Is 20 a whole number?

Yes 20 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 20. Help him in finding the mean of 20.

Factors of 20 are 1, 2, 4, 5, 10, 20.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 20 is 1 + 2 + 4 + 5 + 10 + 20 = 42.
Hence, the mean of factors of 20 is 42 ÷ 6 = 7.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 20? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 10, 20.
Negative factors are -1, -2, -4, -5, -10, -20.

Joey wants to write all the prime factors of 20 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 20 are 2, 2, 5.
So in exponential form it can be written as 22 x 5.

Kevin has been asked to write 5 factor(s) of 20. Can you predict the answer?

5 factor(s) of 20 are 1, 2, 4, 5, 10.

Sammy is puzzled while calculating the prime factors of 20. Can you help him find them?

Factors of 20 are 1, 2, 4, 5, 10, 20.
Prime factors of 20 are 2, 2, 5

What is prime factorization of 20?

Prime factorization of 20 is 2 x 2 x 5 = 22 x 5.

Can you help Rubel to find out the product of the even factors of 20?

Factors of 20 are 1, 2, 4, 5, 10, 20.
Even factors of 20 are 2, 4, 10, 20.
Hence, product of even factors of 20 is; 2 x 4 x 10 x 20 = 1600.