# Factors of 126 in pair

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

#### How to find factors of a number in pair

 1.   Steps to find factors of 126 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 126 in pair

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 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 126 are 1 , 2 , 3 , 6 , 7 , 9 , 14 , 18 , 21 , 42 , 63 , 126. So, factors of 126 in pair are (1,126), (2,63), (3,42), (6,21), (7,18), (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.

#### Steps to find Factors of 126

• Step 1. Find all the numbers that would divide 126 without leaving any remainder. Starting with the number 1 upto 63 (half of 126). The number 1 and the number itself are always factors of the given number.
126 ÷ 1 : Remainder = 0
126 ÷ 2 : Remainder = 0
126 ÷ 3 : Remainder = 0
126 ÷ 6 : Remainder = 0
126 ÷ 7 : Remainder = 0
126 ÷ 9 : Remainder = 0
126 ÷ 14 : Remainder = 0
126 ÷ 18 : Remainder = 0
126 ÷ 21 : Remainder = 0
126 ÷ 42 : Remainder = 0
126 ÷ 63 : Remainder = 0
126 ÷ 126 : Remainder = 0

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

• Is 126 a composite number?

Yes 126 is a composite number.

• Is 126 a prime number?

No 126 is not a prime number.

• What is the mean of factors of 126?

Factors of 126 are 1 , 2 , 3 , 6 , 7 , 9 , 14 , 18 , 21 , 42 , 63 , 126. therefore mean of factors of 126 is (1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 + 126) / 12 = 26.00.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Can you help Rubel in arranging 126 blocks in order to form a rectangle in all possible ways? For arranging 126 blocks in order to form a rectangle in all possible ways we need to find factors of 126 in pair.

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. So, factors of 126 in pair are (1,126), (2,63), (3,42), (6,21), (7,18), (9,14).

Ariel has been asked to write all factor pairs of 126 but she is finding it difficult. Can you help her find out?

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. So, factors of 126 in pair are (1,126), (2,63), (3,42), (6,21), (7,18), (9,14).

How many total number of factors of 126 in pair are possible?

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. Hence, the factors of 126 in pair are (1,126), (2,63), (3,42), (6,21), (7,18), (9,14). Therefore, in total 6 pairs of factors are possible.

Sammy wants to write all the negative factors of 126 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 126 are -1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, -126. Hence, factors of 126 in pair are (-1,-126), (-2,-63), (-3,-42), (-6,-21), (-7,-18), (-9,-14).

Help Deep in writing the positive factors of 126 in pair and negative factor of 126 in pair.

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. Positive factors of 126 in pair are (1,126), (2,63), (3,42), (6,21), (7,18), (9,14). Negative factors of 126 in pair are (-1,-126), (-2,-63), (-3,-42), (-6,-21), (-7,-18), (-9,-14).

Find the product of all factors of 126.

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. So the product of all factors of 126 would be 1 x 2 x 3 x 6 x 7 x 9 x 14 x 18 x 21 x 42 x 63 x 126 = 4001504141376.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 126.
- Writing all prime factors of 126.
- Writing all the possible factors of 126 in pair.
Help him in writing all these.

Positive 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.
Factors of 126 in pair are (1,126), (2,63), (3,42), (6,21), (7,18), (9,14).

Can you help Sammy list the factors of 126 and also find the factor pairs?

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