In this blog post, we will take a closer look at the factors of 49, a composite number. We will delve into the ways in which it can be broken down into its component parts and explore the different methods used to find its factors. In addition, we will also provide information about negative factors of 49, pair factors, prime factorization, and its indivisible factors. We will also explore the concept of factor tree.

## Contents

## Factors Calculator

Factors of 49 | 1, 7 and 49 |

Negative Factors of 49 | -1, -7 and -49 |

Prime Factors of 49 | 7 |

Prime Factorization of 49 | 7 × 7 |

Factors of 49 in Pairs | (1, 49), (7, 7) |

Negative Pair Factors of 49 | (-1, -49), (-7, -7) |

**Prime Numbers**

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Some examples of prime numbers include 2, 3, 5, 7, and 11. Prime numbers are important in mathematics as they are used in many mathematical formulas and algorithms, and are also used in the study of number theory.

**Composite Numbers**

A composite number is a whole number greater than 1 that can be divided evenly by a number other than 1 or itself. In other words, a composite number is not a prime number. Some examples of composite numbers include 4, 6, 8, 9, and 10.

## What are the factors of 49?

The method of calculating the factors of 49 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 49 are the factors of 49.

By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 49 ÷ 1 = 49

This division gives the remainder 0 and so is divisible by 49. So please put them 1 and 49 in your factor list.

1, … 49

(ii) 49 ÷ 2 = 24.5

This division gives the remainder 24.5, not being thoroughly divided. So we will not write 2 and 24.5 on the list.

(iii) 49 ÷ 3 = 16.33

This division gives the remainder 16.33, not being thoroughly divided. So we will not write 3 and 16.33 on the list.

(iv) 49 ÷ 4 = 12.25

This division gives the remainder 12.25, not being thoroughly divided. So we will not write 2 and 12.25 on the list.

(v) 49 ÷ 5 = 9.8

This division gives the remainder 9.8, not being thoroughly divided. So we will not write 5 and 9.8 on the list.

(vi) 49 ÷ 6 = 8.16

This division gives the remainder 8.16, not being thoroughly divided. So we will not write 6 and 8.16 on the list.

(vii) 49 ÷ 7 = 7

This division gives the remainder 0 and so is divisible by 8. So please put them 6 and 8 in your factor list.

1, 7 … 7, 49

(viii) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 7 and 49 are factors of 49.

## Factor pairs of 49

1 x 49 = 49

7 x 7 = 49

So, (1, 49), and (7, 7) are factor pairs of 49

## Factor pairs of -49

-1 x -49 = 49

-7 x -7 = 49

So, (-1, -49), and (-7, -7) are negative pair factors of 49

## Prime Factorization of 49

49 ÷ 7 = 7

7 ÷ 7 = 1

Therefore, 7 x 7 are Prime factorization of 49.

As we saw earlier, the prime factorization of 49 is 7 x 7. When we multiply two identical prime factors, we get a square of that number. Therefore, we can rewrite the prime factorization of 49 as 7². This notation indicates that 7 is raised to the power of 2, which means 7 is multiplied by itself two times.

## Factor tree of 49

```
49
/ \
7 7
```