# Factors of 200

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

#### How to find factors of a number

 1.   Find factors of 200 using Division Method 2.   Find factors of 200 using Prime Factorization 3.   Find factors of 200 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 200

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

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

#### 2. Steps to find factors of 200 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 200 using the division method, follow these steps:

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

So, the prime factorization of 200 is, 200 = 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 200 as shown below:

So, the prime factorization of 200 is, 200 = 2 x 2 x 2 x 5 x 5.

#### 3. Find factors of 200 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 200 would be the two numbers which, when multiplied, give 200 as the result.

The following table represents the calculation of factors of 200 in pairs:

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

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 200. They are called negative pair factors.

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

• What two numbers make 200?

Two numbers that make 200 are 2 and 100.

• What is prime factorization of 200?

Prime factorization of 200 is 2 x 2 x 2 x 5 x 5.

• Write some multiples of 200?

First five multiples of 200 are 400, 600, 800, 1000.

• Which is the smallest prime factor of 200?

The smallest prime factor of 200 is 2.

• Is 200 a perfect square?

No 200 is not a perfect square.

• What is the sum of all factors of 200?

The sum of all factors of 200 is 465.

• What are factors of 200?

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

• How do you find factors of a negative number? ( eg. -200 )?

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

• Is 200 a whole number?

Yes 200 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 200. Help him in finding the mean of 200.

Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 200 is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 200 = 465.
Hence, the mean of factors of 200 is 465 ÷ 12 = 38.75.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 200? Help her in writing all the factors.

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

Joey wants to write all the prime factors of 200 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 200 are 2, 2, 2, 5, 5.
So in exponential form it can be written as 23 x 52.

Kevin has been asked to write 11 factor(s) of 200. Can you predict the answer?

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

Sammy is puzzled while calculating the prime factors of 200. Can you help him find them?

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

What is prime factorization of 200?

Prime factorization of 200 is 2 x 2 x 2 x 5 x 5 = 23 x 52.

Can you help Rubel to find out the product of the even factors of 200?

Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
Even factors of 200 are 2, 4, 8, 10, 20, 40, 50, 100, 200.
Hence, product of even factors of 200 is; 2 x 4 x 8 x 10 x 20 x 40 x 50 x 100 x 200 = 512000000000.