Factors

# Factors of 46 | Prime Factorization of 46 | Factor Tree of 46

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 46 | Prime Factorization of 46 | Factor Tree of 46

Factors of 46: The factors of a number are defined as a set of integers, that can divide a given number evenly.

The number 46 has 4 factors in total. Factors of 46 are 1, 2, 23, and 46.

The factors of all numbers are both positive and negative. They also occur in pairs. So, if we multiply the pairs by each other, the product we get will be equal to 46.

In this article, we will cover information on how to find the factors of 46. We will also look at the prime factorization and factor tree of 46 with solved examples. Keep reading to learn more.

## What Are the Factors of 46?

The factors of 46 are the numbers that divide 46 evenly, leaving no reminder behind. These factors are both positive and negative.

### What Are the Factors of 46 in Pairs?

A pair factor of 46 is a combination of two numbers, which when multiplied by each other yields 46 as the product. These pair factors can also be positive or negative pairs as described in the tables below:

### Positive Pair Factors of 46

Positive pair factors of 46: (1, 46) and (2, 23).

### Negative Pair Factors of 46

Negative pair factors of 46: (-1, -46) and (-2, -23).

### How To Find Factors of 46 Through Division Method?

We are using the division method first, to find the factors of 46. In this method, we will multiply 46 with a sequence of natural numbers. The number that divides 46 fully, without leaving behind a reminder is a factor of 46. The following steps provide a detailed idea about this method:

46 ÷ 1 = 46

46 ÷ 2 = 23

46 ÷ 23 = 2

46 ÷ 46 = 1

Therefore, the factors of 46 are 1, 2, 23, and 46.

### What Is the Prime Factorization of 46?

We will now be using prime factorization to find the factors of 46. First, we will check if the given number is prime or composite. If it is a prime number, it has only two factors: 1 and 46. If not, it has more than two factors.
46 is the composite number. So, it has more than two factors. We can use prime factorization to find the factors of 46.

The steps below present a detailed idea about using prime factorization to find the prime factors of 46:

Step 1: Divide the number 46 by the smallest prime number that can divide it. This number is 2.
46 ÷ 2 = 23

Step 2: We got 23 as the quotient. Dividing 23 with 23 gives us 1.
23 ÷ 23 = 1

1 cannot be divided further so, the prime factors of 46 are 2 X 23
Image representation of the prime factorization of 46:

### What is the Factor Tree of 46?

We will now use the factor tree method to find the prime factors of 46. We will first place 46 on top of the tree. As part of its branches, we will select any pair factor of 46 and write them down. We will then split these pairs further until all the branches contain prime numbers.

Step 1: Let’s place the number 6 on top of the factor tree. Let’s select 2 and 23 as the branches of the factor tree.

Step 2: We can see that 2 and 23 are both prime numbers. So, they can be separated no further. This brings us to the end of the factor tree.
Hence, circling all the branches, 2 X 23 = 46, which are 46 prime factors.
Below is an image representation of the factor tree of 46, choosing 2 and 23 as pair factors of 46.

### Solved Examples of Factors of 46

Here are some solved examples of 46 factors:

What is the sum of all the factors of 46?
1, 2, 23, and 46 are the 46 factors.
1 + 2 + 23 + 46 = 72
Hence, 72 is the sum of all 46 factors.

What are the factors and prime factors of 46?
The factors of 46 are 1, 2, 23 and 46.
The prime factors of 46 are 23 X 2.

What’s the highest common factor between 46 and 69?
The factors of 46 are 1, 2, 23 and 46.
Factors of 69 are 1, 3, 23 and 69.
Hence, from the above, the common factors of 46 and 69 are 1 and 23.
The highest common factor between 46 and 69 is 23.

What’s the highest common factor between 46 and 48?
The factors of 46 are 1, 2, 23, and 46.
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Hence, from the above, the common factors of 46 and 48 are 1 and 2.
The highest common factor between 46 and 48 is 2.

Is 2 a factor of 46?
Yes, 2 is a factor of 46.
As 46 ÷ 23 = 2.

What are the factors of -46?
The factors of -46 are -1, -2, -23, and -46.

What are the common factors of 46 and 100?
To find the common factors of 46 and 100, we need to find the factors of both numbers.
Factors of 46: 1, 2, 23 and 46
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100
Hence the common factors of 46 and 100 are 1 and 2.

What are all the factors of 46?
The factors of 46 are 1, 2, 23, and 46.

What are the factors of 46 that are composite?
Any number which has more than 2 factors is known as a composite number.
The only number which has more than 2 factors in factors of 46 is 46.

What factors of 46 are multiples of 2?
The factors of 42 that are multiples of 2 are 2 and 46.
2 x 1 = 2
2 x 23 = 46.

How many 46 factors are odd?
A total of 2 odd numbers are there in factors of 46 and they are 1 and 23.

What are the factors of 46 and 184?
The factors of 46 are 1, 2, 23, and 46.
The factors of 184 are 1, 2, 4, 8, 23, 46, 92, and 184.

What are the common factors of 46 and 32?
To list out the common factors of 46 and 32, we need to find the factors of both numbers.
Factors of 46: 1, 2, 23 and 46
Factors of 32: 1, 2, 4, 8, 16 and 32
From the above, the common factors of 46 and 32 are 1 and 2.

How many different factors are there for the number 46?
A total of 4 factors are there for the number 46 and they are 1, 2, 23 and 46.

How many pair factors are there in 46?
A total of 2 pairs are there in factors of 46.

What is the largest factor of 46?
The largest factor of 46 is 46.
The second largest factor of 46 is 23.

### FAQs on Factors of 46

List all the factors of 46
1, 2, 23, and 46 are the 46 factors.

What are the composite factors of 46?
46 is the only composite factor of 46. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 46 in pairs?
(1, 46) and (2, 23) are the 46 factors of pairs.

What are the positive factors for 46?
1, 2, 23, and 46 are the positive factors for 46.

Is 24 a factor of 46?
No, 24 is not a factor of 46. 24 does not divide 46 evenly and it leaves behind a reminder. So, it is not a factor.

We have now covered all the information that we need on the factor of 46. We hope that this blog was useful and easy to understand.

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Written by by

Prerit Jain

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