# Factors of 46

Understanding Prime and Composite Numbers When studying mathematics, one of the fundamental concepts that students learn is that of prime and composite numbers. In this article, we will delve into the factors of 46, a composite number, and explore the various ways in which it can be broken down into its component parts.

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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 46?

The method of calculating the factors of 46 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 46 are the factors of 46.
By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 46 ÷ 1 = 46

This division gives the remainder 0 and so is divisible by 46. So please put them 1 and 46 in your factor list.

1, …. 46

(ii) 46 ÷ 2 = 23

This division gives the remainder 0 and so is divisible by 23. So please put them 2 and 23 in your factor list.

1, 2 …. 23, 46

This division gives the remainder 22.5, not being thoroughly divided. So we will not write 2 and 22.5 on the list.

(iii) 46 ÷ 3 = 15.33

This division gives the remainder 15.33, not being thoroughly divided. So we will not write 3 and 15.33 on the list.

(iv) 46 ÷ 4 = 11.5

This division gives the remainder 11.5, not being thoroughly divided. So we will not write 4 and 11.5 on the list.

(iv) 46 ÷ 5 = 9.2

This division gives the remainder 9.2, not being thoroughly divided. So we will not write 5 and 9.2 on the list.

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

So 1, 2, 23 and 46 are factors of 46.

## Factor pairs of 46

1 x 46 = 46
2 x 23 = 46

So, (1, 46) and (2, 23) are factor pairs of 46

## Factor pairs of -46

-1 x -46 = 46
-2 x -23 = 46

So, (-1, -46) and (-2, -23) are negative pair factors of 46

## Prime Factorization of 46

46 ÷ 2 = 23
23 ÷ 23 = 1

Therefore, 2 x 23 are Prime factorization of 46.

## Factor tree of 46

``````    46
/  \
2   23``````