Factors of 126
Factors are whole numbers or integers that are multiplied together to give a number. If p × q = d, then p and q are factors of d. Let us say you wish to find the factors of 126. First of all you will find all pairs of those numbers which when multiplied together give 126. Factors and multiples of a number can be expressed together. For example, 126 is a multiple of 6 this means 6 is a factor of 126. In another word, factoring a number is like taking or separating a number apart. It is always meant to express as the product of its factors. Factors of numbers are either composite numbers or prime numbers. If we talk about 126, it has 12 factors, which means 126 is a composite number.
 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
 Prime Factorization of 126: 2 × 3 × 3 × 7
Let us explore more about factors of 126 and ways to find them.
1.  What Are the Factors of 126? 
2.  How to Calculate Factors of 126? 
3.  Factors of 126 in Pairs 
4.  FAQs on Factors of 126 
What Are the Factors of 126?
Factors of a number, are the numbers that divide the given number exactly without any remainder. According to the definition of factors, the factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. So,126 is a composite number as it has factors other than 1 and itself. Let us learn various methods to find the factors of 126.
How to Calculate Factors of 126?
We can use different methods like divisibility test, prime factorization, and the upsidedown division method to calculate the factors of 126. In prime factorization, we express 126 as a product of its prime factors, and in the division method, we see which numbers divide 126 exactly without a remainder.
Let us calculate factors of 126 using follwoing two methods:
 Factors of 126 by prime factorization factor tree method
 Factors of 126 by upsidedown division method
Prime Factorization by UpsideDown Division Method
As per the definition of prime factorization, we need to find the product of prime factors of the number. Let us see the prime factorization of 126.
Prime Factorization by Factor Tree Method
Like prime factorization using upsidedown division method, we can find the prime factors of a number using factor tree method. In this method we use the multiplication process by breaking a number into its factor pairs. In the pair, one factor is always prime.
Here 2, 3, and 7 are prime factors of 126.
Explore factors using illustrations and interactive examples
 Factors of 121: The factors of 121 are 1, 11, and 121.
 Factors of 125: The factors of 125 are 1, 5, 25, and 125.
 Factors of 128: The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
 Factors of 216: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
 Factors of 63: The factors of 63 are 1, 3, 7, 9, 21, and 63.
Factors of 126 in Pairs
To find factors of 126 in pairs, we need to find such pairs of factors and whole numbers which, when multiplied together, give 126 as a result. Factor pairs of 126 can be negative as well as positive.
Positive factor pairs of 126 are:
 1 × 126 = 126
 2 × 63 = 126
 3 × 42 = 126
 6 × 21 = 126
 7 × 18 = 126
 9 × 14 = 126
 So the positive factor pairs of 126 are (1 × 126), (2 × 63), (3 × 42), (6 × 21), (7 × 18), and (9 × 14).
Negative factor pairs of 126 are:
 1 × 126 = 126
 2 × 63 = 126
 3 × 42 = 126
 6 × 21 = 126
 7 × 18 = 126
 9 × 14 = 126
 So the negative factor pairs of 126 are (1 × 126), (2 × 63), (3 × 42), (6 × 21), (7 × 18), and (9 × 14).
Important Notes:
 Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
 The positive factor pairs of 126 are (1 × 126), (2 × 63), (3 × 42), (6 × 21), (7 × 18), and (9 × 14).
 The negative factor pairs of 126 are (1 × 126), (2 × 63), (3 × 42), (6 × 21), (7 × 18), and (9 × 14).
Challenging Questions:
 Prove that decimal numbers cannot be factors of 126.
 Prove that fractions or the numbers in form of p/q cannot be factors of 126.
 Can the factor of a number be greater than the number itself?
Solved Examples

Example 1: Can you help Jim divide 126 candies evenly among 42 kids?
Solution:
Total number of kids = 42
Total number of candies = 126
Candies per kid = 126 ÷ 42 = 3
Here, 3 and 42 are factors of 126. 
Example 2: Can you help Tayo in finding average of the sum of prime factors of 126?
Solution:
The prime factors of 126 are = 2, 3, and 7
Sum of prime factors of 126 is = 2 + 3 + 7 = 12
Average of sum of prime factors of 126 is = 12 ÷ 3 = 4
FAQs on Factors of 126
What are the prime factors of 126?
The prime factors of 126 are 2, 3, and 7.
Is 126 a square number?
No, 126 is not a square number; its square root is an irrartional number.
Which is the smallest factor of 126?
Smallest factor of 126 is 1.
Which is the highest factor of 126?
The highest factor of 126 is 126 itself.
What are the common factors of 126 and 6?
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
The factors of 6 are 1, 2, 3, and 6.
Common factors of 126 and 6 are 1, 2, 3, and 6.
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