Factorization Formula
The factorization formula is used to factorize a number. Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number. The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself. Let us learn more about the factorization formula using solved examples in the following sections.
What is Factorization Formula?
The factorization formula factorizes a number quickly into smaller numbers or factors of the number. A factor is a number that divides the given number without any remainder. The factorization formula of a given value can be expressed as,
N = X^{a} × Y^{b} × Z^{c}
where,
 N = Any number
 X, Y, and Z = Factors of number N
 a, b, and c = exponents of factors X, Y, and Z respectively

Example 1: Sam wants to factorize number 40. What the prime factorization of 40? Solve it by using the factorization formula.
Solution:
To find: Prime factorization of 40.
Using Factorization Formula,
Factorization Formula for any number, N = X^{a} × Y^{b} × Z^{c}
40 = 2 × 2 × 2 × 5
= 2^{3 }× 5
Answer: The prime factorization of 40 is 2^{3 }× 5.

Example 2: If the factorization of a number is 2 × 2 × 3 × 5. Find the number by using the factorization formula.
Solution:
To find: The factorized number
Given:
The factorization of a number = 2 × 2 × 3 × 5
Using the Factorization Formula,
Factorization Formula for any number, N = X^{a} × Y^{b} × Z^{c}
= ( 2 × 2 × 3 × 5) units
= 60
Answer: The factorized number is 60.