Find Prime Factorization/Factors Of 126 - Cuemath

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 upside-down 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 upside-down division method

Prime Factorization by Upside-Down 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 upside-down 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?