# Factors of Composite Numbers Important Formulas, Definitions, & Examples:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Number System Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

#### What are Composite numbers:

All-natural numbers that are greater than 1 but not the prime numbers are known as composite numbers, also a composite number must have more than two factors. 1 is not a composite number. The numbers {4, 6, 8, 9, 10, 12, 14, 15,.........} are the composite numbers. A Composite number can be factorized into more than two prime factors.

#### Factors of Composite Numbers:

The number $$9$$ which is a composite number, can be factorized into two prime factors $$(3 \times 3)$$. Here the composite number $$9$$ have $$3$$ factors 1, 3, and 9.

The composite number $$18$$ can be factorized into three prime factors $$(2 \times 3 \times 3)$$. Here the composite number $$18$$ have $$6$$ factors 1, 2, 3, 6, 9, and 18.

now we are going to discuss how to find out factors of a composite number by using a formula.

#### Formula to find the factors of a composite number:

$$Composite \ Numbers \ = A_{1}^{x_1} \times A_{2}^{x_2} \times A_{3}^{x_3} \times A_{4}^{x_4} \times ........A_{n}^{x_n}$$

Composite Numbers = $$A_{1}^{x_1} \times A_{2}^{x_2} \times A_{3}^{x_3} \times A_{4}^{x_4} \times ........A_{n}^{x_n}$$

Where, $$A_1, A_2, A_3, A_4,..............A_n$$ are prime factors, and $$x_1, x_2, x_3, x_4,..............x_n$$ are their respective powers.

now to find the factors of a composite number, add 1 in every respective power of prime numbers.

$$Factors \ = (x_1 + 1) \times (x_2 + 1) \times (x_3 + 1) \times (x_4 + 1) \times...............(x_n + 1)$$

$$(x_1 + 1) \times (x_2 + 1) \times (x_3 + 1) \\ \times (x_4 + 1) \times............(x_n + 1)$$

#### Factors of Composite Numbers, Examples:

Example(1): Find the factors of composite number $$250$$?

Solution: Factors of composite number $$250 = 2 \times 5 \times 5 \times 5 = 2^1 \times 5^3$$

Where, $$A_1 = 2$$, $$A_2 = 5$$ are prime numbers, and $$x_1 = 1$$, $$x_2 = 3$$ are their respective powers.

Now factors of composite number $$= (x_1 + 1) \times (x_2 + 1)$$ $$= (1 + 1) \times (3 + 1) = 2 \times 4 = 8$$, here we found the factors of composite number $$250$$ are $$8$$.

Example(2): Find the factors of composite number $$180$$?

Solution: Factors of composite number $$180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5^1$$

Where, $$A_1 = 2$$, $$A_2 = 3$$ and $$A_3 = 5$$ are prime numbers, and $$x_1 = 2$$, $$x_2 = 2$$ and $$x_3 = 1$$ are their respective powers.

Now factors of composite number $$= (x_1 + 1) \times (x_2 + 1) \times (x_3 + 1)$$ $$= (2 + 1) \times (2 + 1) \times (1 + 1)$$ $$= 3 \times 3 \times 2 = 18$$, here we found the factors of composite number $$180$$ are $$18$$.

#### Factors of Prime numbers:

Any single prime number has only two factors $$1$$, and the number itself, like $$5$$ is a prime number and has only two factors $$1$$, and itself. A prime number can not be a composite number.

Example(3): Find the factors of composite number $$47$$?

Solution: Factors of composite number $$47 = 47^1$$

Where, $$A_1 = 2$$ is a prime number, and $$x_1 = 1$$ is their respective power.

Hence factors of composite number $$= (x_1 + 1)$$ $$= (1 + 1) = 2$$, here we found the factors of composite number $$47$$ are $$2$$, The number 47 itself and 1.