Factors

# Factors of 49

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 49

The factors of 49 are 1, 7, and 49. These numbers are known as the factors of 49 since when we multiply a combination of these numbers, it gives back the number 49. For example, 7 x 7 results in the number 49. Also, these factors are both positive and negative. Let us learn how to find the factors, prime factors, and pair factors of 49 along with solved examples. Scroll down to read more.

## What Are the Factors of 49?

Factors of any number are the numbers that divide the number entirely without leaving any remainder. If the given number is a prime number, it has only two prime factors, 1 and the number itself. Alternatively, if the given number is a composite number, it implies that the number will have more than two factors.

Since 49 is a composite number, it has multiple factors, and they are:

## What are the Factors of 49 in Pairs?

A pair of 49 factors is a combination of two numbers that results in the numeral 49 after the multiplication of two numbers. They can either be a positive or negative pair. Here are the positive and negative pairs of 49.

### Positive Pair Factors of 49

The positive pair factors of 49 are given below:

### Negative Pair Factors of 49

The negative pair factors of 49 are given below:

## How To Find Factors of 49 by Division Method?

You will be using the division method to find the factors of 49. Divide 49 by all the numbers from 1 to 49. The numbers which leave a remainder are not a factor of 49. Those numbers which don’t leave any remainder are the factors of 49.

• 49 ÷ 1 = 49
• 49 ÷ 7 = 7
• 49 ÷ 49 = 1

Hence from the above, it is evident that factors of 49 are 1, 7 and 49.

Since the number 49 is large, the division method is a lengthy method to find the factors.

## What Are Prime Factors of 49?

Since 49 is a composite number, let’s find the prime factorization of 49.

• Step 1: Divide 49 with the smallest factor of 49 which is a prime number. In this case, therefore, we will divide 49 by 7.
• Step 2: Now divide the multiple again by the smallest prime number which is 7.
7 ÷ 7 = 1

So, in conclusion, we can see that 7 x 7 is the prime factorization of 49. It means that 7 and 7 are the prime factors of 49.

## What Is the Prime Factor Tree for 49?

Students can also use the factor tree method to find the prime factors of 49. In a factor tree, we divide a number until the answer becomes 1, and the factors are written in the form of branches of a tree. Then, the last factors are circled, and they are the prime factors of the number. The detailed steps on how to do this are explained below:

• Step 1: Let’s place the number 49 at the top and write down 49 in pairs, that is, 7 and 7.
• Step 2: The branches in the factor tree will now be all the prime numbers.
• Step 3: Circling all the branches, 7 x 7 = 49, which are 49 prime factors.

## Solved Examples on Factors of 49

Here are some solved examples that include common questions and answers to make your concepts clearer.

What are the factors of 49 that add up to 8?
To find the factors of 49 that add up to 8, we need to list out all the factors.
The factors of 49 are 1, 7, and 49. After adding them in combinations, you can find the factors that make 8 and they are:
1 + 7 = 8
So, 1 and 7 are the factors of 49 that add up to 8.

What are the pair factors of 49?
There are only two pair factors of 49. The pair is (1, 49) and (7, 7)

What is the sum of the prime factors of 49?
The prime factors of 49 are 7, and 7.
Adding the prime factors 7 + 7 = 14.
Hence the sum of the prime factors of 49 is 14.

What is the sum of all factors of 49?
To find the sum of all the factors of 49, we need to add all the 49 factors i.e. 1,7 and 49.
Adding 1 + 7 + 49 = 57.
Hence the sum of all the factors 49 is 57.

What are the common factors of 49 and 14?
Factors of 49: 1, 7, and 49
Factors of 14: 1, 2, 7, and 14
Hence, the common factors of 49 and 14 are 1 and 7.

What are the common factors of 49 and 70?
Factors of 49: 1, 7, and 49
Factors of 70: 1, 2, 5, 7, 10, 14, 35, and 70
Common factors of 49 and 70 are 1, and 7.

What are the common factors of 49 and 81?
Factors of 49: 1, 7, and 49
Factors of 81: 1, 3, 9, 27 and 81
The common factor of 49 and 81 is 1.

## FAQs on Factors of 49

List all the factors of 49
1, 7, and 49 are the factors of 49.

What are the composite factors of 49?
Composite numbers are the ones that are described as whole digits and have three or more whole number factors.
49 is the only composite factor of 49.

What are the prime factors of 49?
7 × 7 are the prime factors of 49.

What are the common factors of 49?
1, 7, and 49 are the common factors of 49.

What are the positive factors of 49?
(1, 49), and (7, 7) are the positive factors of 49.

We hope this article about determining the factors of 49 has been useful to you. If you have any questions or concerns, please share those in the comments section below, and we will get back to you with the required information.

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