# Prime factors

The factors that are prime numbers, are the prime factors.

## Introduction

Every quantity can be factored as two or more factors by the factorization. The factors, which are prime numbers, are called the prime factors of the quantity. The prime factors can be identified from the factors in two simple steps.

1. Write factors of a number.
2. Identify the prime numbers in the factors of the quantity.

### Example

$48$ is a number and factorise this number by factoring method.

$(1) \,\,\,$ $48 \,=\, 1 \times 48$
$1$ and $48$ are factors of $48$

$(2) \,\,\,$ $48 \,=\, 2 \times 24$
$2$ and $24$ are factors of $48$

$(3) \,\,\,$ $48 \,=\, 3 \times 16$
$3$ and $16$ are factors of $48$

$(4) \,\,\,$ $48 \,=\, 4 \times 12$
$4$ and $12$ are factors of $48$

$(5) \,\,\,$ $48 \,=\, 6 \times 8$
$6$ and $8$ are factors of $48$

$1$, $2$, $3$, $4$, $6$, $8$, $12$, $16$, $24$ and $48$ are factors of the number $48$. The factors of $48$ is denoted by $F_{48}$ in mathematical form.

$F_{48}$ $\,=\,$ $1$, $2$, $3$, $4$, $6$, $8$, $12$, $16$, $24$ and $48$

Now, identify the prime numbers from the list of factors of the quantity $48$.

There are ten factors for the number $48$ but $2$ and $3$ are prime numbers. Therefore, the factors $2$ and $3$ are called the prime factors of $48$.

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