Factors of 46 | Pair Factors & Prime Factorization

Factors of 46

When we multiply 2 and 8, we get 16, i.e., 2 × 8 = 16. Here, 2 and 8 are the factors of 16. In the same way, we can calculate the factors of 46. The factors of 46 are the numbers (both positive and negative numbers) that multiply and give 46 as the result. 

In this article, I am going to explain how to find the factors of the number 46 and the prime factors of 46 in detail. I hope you will understand it.

What are the Factors of 46?

Factors of 46 are all the integers into which we can evenly divide 46. We know that when a number is divided by its factor, it will equal another factor. Thus, if we divide 46 by its factor, it will equal another factor.

Since 46 is a composite number, it has more than two factors. Therefore, it contains other factors besides 1 and 46.

As a result, factors of 46 are its exact divisors.

What are the Factors of -46?

When we multiply two numbers, and we get -46 as a product, those numbers are the factors of -46. 

Here is the explanation:

-1 × 46 = -46

 1 × -46 = -46

 -2 × 23 = -46

 2 × -23 = -46

 -23 × 2 = -46

 23 × -2 = -46

-46 × 1 = -46

 46 × -1 = -46

We can get -46 by having(-1, 46), (-2, 23), (-23, 2), and (-46, 1) as a pair of factors. Similarly, we can also get -46 by having(1, -46), (2, -23), (23, -2), and (46, -1)as a pair of factors.

How to Calculate the Factors of 46?

You can find factors of 46 by following the steps below.

Step 1: 

In your notebook, write the number 46 first.

Step 2: 

Multiply the two numbers, for example, 2 and 23, to get 46, such as 

2 × 23 = 46.

Step 3: 

It is known that 2 is a prime number that has only two factors: 1 and 2. Therefore, we can’t factorize it any further.

2 = 1 × 2

Step 4: 

Similarly, 23 is a prime number and can’t be factorized.

23 = 1 × 23

Step 5: 

So, the factorization of 46 produces 1 × 2 × 23.

We obtain the following unique numbers here: 1, 2, 23 and 46

Factor pairs of 46

You can find the pair factors of 46 by multiplying the two numbers in a pair to get the original number of 46. 

Such numbers are as follows:

Thus, the positive factors of 46 are 1, 2, 23, and 46.

Also, the negative pair factors of 46 are (-1, -46), (-2, -23), (-23, -2), and (-46, -1).

Hence, the negative factors of the number 46 are -1, -2, -23, and -46.

Interesting Facts about factors 46:

• The sum of all factors of 46 is 72:

 1 + 2 + 23 + 46 = 72.

• The number 46 contains only one even factor other than 46 and only one odd factor other than 1.
• The product of all the factors of 46 is equal to the square of 46, which means: 

1 × 2 × 23 × 46 = 46 × 46 = 462 = 2116.

How to calculate Prime Factors of 46?

We can write the prime factors of 46 as follows using prime factorization.

As a first step, divide 46 by the smallest prime number, 2, i.e. 2.

46 ÷ 2 = 23

Since 2 and 23 are prime numbers, we cannot use the division method.

As a result, 46 can be factorized by 2 × 23.

Solved Examples 

Example 1:

What are the common factors between 16 and 24?

Solution:

Factors of 16 are 1, 2, 4, 8, and 16.

1, 2, 3, 4, 6, 8, 12, and 24 are the factors of 24.

Hence, 16 and 24 have a common factor of 1, 2, 4, and 8.

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