# Factors of 126

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126

#### How to find factors of a number

 1.   Find factors of 126 using Division Method 2.   Find factors of 126 using Prime Factorization 3.   Find factors of 126 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 126

• Divide 126 by 1: 126 ÷ 1 : Remainder = 0
• Divide 126 by 2: 126 ÷ 2 : Remainder = 0
• Divide 126 by 3: 126 ÷ 3 : Remainder = 0
• Divide 126 by 6: 126 ÷ 6 : Remainder = 0
• Divide 126 by 7: 126 ÷ 7 : Remainder = 0
• Divide 126 by 9: 126 ÷ 9 : Remainder = 0
• Divide 126 by 14: 126 ÷ 14 : Remainder = 0
• Divide 126 by 18: 126 ÷ 18 : Remainder = 0
• Divide 126 by 21: 126 ÷ 21 : Remainder = 0
• Divide 126 by 42: 126 ÷ 42 : Remainder = 0
• Divide 126 by 63: 126 ÷ 63 : Remainder = 0
• Divide 126 by 126: 126 ÷ 126 : Remainder = 0

Hence, Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126

#### 2. Steps to find factors of 126 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 126 using the division method, follow these steps:

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

So, the prime factorization of 126 is, 126 = 2 x 3 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 126 as shown below:

So, the prime factorization of 126 is, 126 = 2 x 3 x 3 x 7.

#### 3. Find factors of 126 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 126 would be the two numbers which, when multiplied, give 126 as the result.

The following table represents the calculation of factors of 126 in pairs:

Factor Pair Pair Factorization
1 and 126 1 x 126 = 126
2 and 63 2 x 63 = 126
3 and 42 3 x 42 = 126
6 and 21 6 x 21 = 126
7 and 18 7 x 18 = 126
9 and 14 9 x 14 = 126

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 126. They are called negative pair factors.

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

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 126 is a factor of itself.
• 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, 6, 7, 9, 14, 18, 21, 42, 63, 126 are exact divisors of 126.
• 1 is a factor of every number. Eg. 1 is a factor of 126.
• Every number is a factor of zero (0), since 126 x 0 = 0.

• Which is the smallest prime factor of 126?

Smallest prime factor of 126 is 2.

• Is 126 a perfect square?

No 126 is not a perfect square.

• What are five multiples of 126?

First five multiples of 126 are 252, 378, 504, 630, 756.

• What is prime factorization of 126?

Prime factorization of 126 is 2 x 3 x 3 x 7.

• What are factors of 126?

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.

• How do you find factors of a negative number? ( eg. -126 )?

Factors of -126 are -1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, -126.

• Is 126 a whole number?

Yes 126 is a whole number.

• Which is greatest factor of 126?

The greatest factor of 126 is 63.

• What are the prime factors of 126?

The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Prime factors of 126 are 2, 3, 3, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 126. Can you help her?

Prime factors of 126 are 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 126?

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Even factors of 126 are 2, 6, 14, 18, 42, 126.
Hence, product of even factors of 126 is; 2 x 6 x 14 x 18 x 42 x 126 = 16003008.

Joy wants to calculate mean of all the factors of 126. Help him in finding the mean of 126.

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 126 is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 + 126 = 312.
Hence, the mean of factors of 126 is 312 ÷ 12 = 26.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 126? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Negative factors are -1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, -126.

How many factors are there for 126?

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

Joey wants to write all the prime factors of 126 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 126 are 2, 3, 3, 7.
So in exponential form it can be written as 2 x 32 x 7.

Kevin has been asked to write 11 factor(s) of 126. Can you predict the answer?

11 factor(s) of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63.