# Factors of 400

Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400

#### How to find factors of a number

 1.   Find factors of 400 using Division Method 2.   Find factors of 400 using Prime Factorization 3.   Find factors of 400 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 400

• Divide 400 by 1: 400 ÷ 1 : Remainder = 0
• Divide 400 by 2: 400 ÷ 2 : Remainder = 0
• Divide 400 by 4: 400 ÷ 4 : Remainder = 0
• Divide 400 by 5: 400 ÷ 5 : Remainder = 0
• Divide 400 by 8: 400 ÷ 8 : Remainder = 0
• Divide 400 by 10: 400 ÷ 10 : Remainder = 0
• Divide 400 by 16: 400 ÷ 16 : Remainder = 0
• Divide 400 by 20: 400 ÷ 20 : Remainder = 0
• Divide 400 by 25: 400 ÷ 25 : Remainder = 0
• Divide 400 by 40: 400 ÷ 40 : Remainder = 0
• Divide 400 by 50: 400 ÷ 50 : Remainder = 0
• Divide 400 by 80: 400 ÷ 80 : Remainder = 0
• Divide 400 by 100: 400 ÷ 100 : Remainder = 0
• Divide 400 by 200: 400 ÷ 200 : Remainder = 0
• Divide 400 by 400: 400 ÷ 400 : Remainder = 0

Hence, Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400

#### 2. Steps to find factors of 400 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 400 using the division method, follow these steps:

• Step 1. Start dividing 400 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 400, which is 2. Divide 400 by 2 to obtain the quotient (200).
400 ÷ 2 = 200
• Step 3. Repeat step 1 with the obtained quotient (200).
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 400 is, 400 = 2 x 2 x 2 x 2 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 400 as shown below:

So, the prime factorization of 400 is, 400 = 2 x 2 x 2 x 2 x 5 x 5.

#### 3. Find factors of 400 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 400 would be the two numbers which, when multiplied, give 400 as the result.

The following table represents the calculation of factors of 400 in pairs:

Factor Pair Pair Factorization
1 and 400 1 x 400 = 400
2 and 200 2 x 200 = 400
4 and 100 4 x 100 = 400
5 and 80 5 x 80 = 400
8 and 50 8 x 50 = 400
10 and 40 10 x 40 = 400
16 and 25 16 x 25 = 400
20 and 20 20 x 20 = 400

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 400. They are called negative pair factors.

Hence, the negative pairs of 400 would be ( -1 , -400 ) , ( -2 , -200 ) , ( -4 , -100 ) , ( -5 , -80 ) , ( -8 , -50 ) , ( -10 , -40 ) , ( -16 , -25 ) and ( -20 , -20 ) .

#### 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. 400 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 400.
• Every number is a factor of zero (0), since 400 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, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are exact divisors of 400.
• Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. Each factor divides 400 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 are all less than or equal to 400.

• Is 400 a perfect square?

Yes 400 is a perfect square.

• What are factors of 400?

Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.

• Which is greatest factor of 400?

The greatest factor of 400 is 200.

• What is the sum of all factors of 400?

The sum of all factors of 400 is 961.

• What are multiples of 400?

First five multiples of 400 are 800, 1200, 1600, 2000.

• What is the greatest prime factors of 400?

The greatest prime factor of 400 is 5.

• What are six multiples of 400?

First five multiples of 400 are 800, 1200, 1600, 2000, 2400, 2800.

• What is prime factorization of 400?

Prime factorization of 400 is 2 x 2 x 2 x 2 x 5 x 5.

• Is 400 a whole number?

Yes 400 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 400? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
Negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -200, -400.

Can you help Sammy find out the product of the odd factors of 400?

Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
Odd factors of 400 are 1, 5, 25.
Hence product of odd factors of 400 is; 1 x 5 x 25 = 125.

Joey wants to write all the prime factors of 400 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 400 are 2, 2, 2, 2, 5, 5.
So in exponential form it can be written as 24 x 52.

How many factors are there for 400?

Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
So there are in total 15 factors.

Kevin has been asked to write 14 factor(s) of 400. Can you predict the answer?

14 factor(s) of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200.

Sammy is puzzled while calculating the prime factors of 400. Can you help him find them?

Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400.
Prime factors of 400 are 2, 2, 2, 2, 5, 5

What is prime factorization of 400?

Prime factorization of 400 is 2 x 2 x 2 x 2 x 5 x 5 = 24 x 52.