# Factors of 252

Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252

#### How to find factors of a number

 1.   Find factors of 252 using Division Method 2.   Find factors of 252 using Prime Factorization 3.   Find factors of 252 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 252

• Divide 252 by 1: 252 ÷ 1 : Remainder = 0
• Divide 252 by 2: 252 ÷ 2 : Remainder = 0
• Divide 252 by 3: 252 ÷ 3 : Remainder = 0
• Divide 252 by 4: 252 ÷ 4 : Remainder = 0
• Divide 252 by 6: 252 ÷ 6 : Remainder = 0
• Divide 252 by 7: 252 ÷ 7 : Remainder = 0
• Divide 252 by 9: 252 ÷ 9 : Remainder = 0
• Divide 252 by 12: 252 ÷ 12 : Remainder = 0
• Divide 252 by 14: 252 ÷ 14 : Remainder = 0
• Divide 252 by 18: 252 ÷ 18 : Remainder = 0
• Divide 252 by 21: 252 ÷ 21 : Remainder = 0
• Divide 252 by 28: 252 ÷ 28 : Remainder = 0
• Divide 252 by 36: 252 ÷ 36 : Remainder = 0
• Divide 252 by 42: 252 ÷ 42 : Remainder = 0
• Divide 252 by 63: 252 ÷ 63 : Remainder = 0
• Divide 252 by 84: 252 ÷ 84 : Remainder = 0
• Divide 252 by 126: 252 ÷ 126 : Remainder = 0
• Divide 252 by 252: 252 ÷ 252 : Remainder = 0

Hence, Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252

#### 2. Steps to find factors of 252 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 252 using the division method, follow these steps:

• Step 1. Start dividing 252 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 252, which is 2. Divide 252 by 2 to obtain the quotient (126).
252 ÷ 2 = 126
• Step 3. Repeat step 1 with the obtained quotient (126).
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 252 is, 252 = 2 x 2 x 3 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 252 as shown below:

So, the prime factorization of 252 is, 252 = 2 x 2 x 3 x 3 x 7.

#### 3. Find factors of 252 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 252 would be the two numbers which, when multiplied, give 252 as the result.

The following table represents the calculation of factors of 252 in pairs:

Factor Pair Pair Factorization
1 and 252 1 x 252 = 252
2 and 126 2 x 126 = 252
3 and 84 3 x 84 = 252
4 and 63 4 x 63 = 252
6 and 42 6 x 42 = 252
7 and 36 7 x 36 = 252
9 and 28 9 x 28 = 252
12 and 21 12 x 21 = 252
14 and 18 14 x 18 = 252

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 252. They are called negative pair factors.

Hence, the negative pairs of 252 would be ( -1 , -252 ) , ( -2 , -126 ) , ( -3 , -84 ) , ( -4 , -63 ) , ( -6 , -42 ) , ( -7 , -36 ) , ( -9 , -28 ) , ( -12 , -21 ) and ( -14 , -18 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 252 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 252.
• Every number is a factor of zero (0), since 252 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, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252 are exact divisors of 252.
• Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252. Each factor divides 252 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252 are all less than or equal to 252.

• Which is the smallest prime factor of 252?

Smallest prime factor of 252 is 2.

• Is 252 a perfect square?

No 252 is not a perfect square.

• What are five multiples of 252?

First five multiples of 252 are 504, 756, 1008, 1260, 1512.

• What is prime factorization of 252?

Prime factorization of 252 is 2 x 2 x 3 x 3 x 7.

• What are factors of 252?

Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.

• How do you find factors of a negative number? ( eg. -252 )?

Factors of -252 are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, -252.

• Is 252 a whole number?

Yes 252 is a whole number.

• Which is greatest factor of 252?

The greatest factor of 252 is 126.

• What are the prime factors of 252?

The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
Prime factors of 252 are 2, 2, 3, 3, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 252. Can you help her?

Prime factors of 252 are 2, 2, 3, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 252?

Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
Even factors of 252 are 2, 4, 6, 12, 14, 18, 28, 36, 42, 84, 126, 252.
Hence, product of even factors of 252 is; 2 x 4 x 6 x 12 x 14 x 18 x 28 x 36 x 42 x 84 x 126 x 252 = 16390160963076096.

Joy wants to calculate mean of all the factors of 252. Help him in finding the mean of 252.

Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 252 is 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 63 + 84 + 126 + 252 = 728.
Hence, the mean of factors of 252 is 728 ÷ 18 = 40.44.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 252? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
Negative factors are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, -252.

How many factors are there for 252?

Factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
So there are in total 18 factors.

Joey wants to write all the prime factors of 252 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 252 are 2, 2, 3, 3, 7.
So in exponential form it can be written as 22 x 32 x 7.

Kevin has been asked to write 17 factor(s) of 252. Can you predict the answer?

17 factor(s) of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126.