# Factors of 49

Factors of 49 are 1, 7, and 49

#### How to find factors of a number

 1.   Find factors of 49 using Division Method 2.   Find factors of 49 using Prime Factorization 3.   Find factors of 49 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 49

• Divide 49 by 1: 49 ÷ 1 : Remainder = 0
• Divide 49 by 7: 49 ÷ 7 : Remainder = 0
• Divide 49 by 49: 49 ÷ 49 : Remainder = 0

Hence, Factors of 49 are 1, 7, and 49

#### 2. Steps to find factors of 49 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 49 using the division method, follow these steps:

• Step 1. Start dividing 49 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 49, which is 7. Divide 49 by 7 to obtain the quotient (7).
49 ÷ 7 = 7
• Step 3. Repeat step 1 with the obtained quotient (7).
7 ÷ 7 = 1

So, the prime factorization of 49 is, 49 = 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 49 as shown below:

So, the prime factorization of 49 is, 49 = 7 x 7.

#### 3. Find factors of 49 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 49 would be the two numbers which, when multiplied, give 49 as the result.

The following table represents the calculation of factors of 49 in pairs:

Factor Pair Pair Factorization
1 and 49 1 x 49 = 49
7 and 7 7 x 7 = 49

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 49. They are called negative pair factors.

Hence, the negative pairs of 49 would be ( -1 , -49 ) , ( -7 , -7 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 7, 49 are exact divisors of 49.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 49 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 49.

• Is 49 a perfect square?

Yes 49 is a perfect square.

• What are factors of 49?

Factors of 49 are 1, 7, 49.

• Which is greatest factor of 49?

The greatest factor of 49 is 7.

• What is the sum of all factors of 49?

The sum of all factors of 49 is 57.

• What are multiples of 49?

First five multiples of 49 are 98, 147, 196, 245.

• What is the greatest prime factors of 49?

The greatest prime factor of 49 is 7.

• What are six multiples of 49?

First five multiples of 49 are 98, 147, 196, 245, 294, 343.

• What is prime factorization of 49?

Prime factorization of 49 is 7 x 7.

• Is 49 a whole number?

Yes 49 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 49? Help her in writing all the factors.

Positive factors are 1, 7, 49.
Negative factors are -1, -7, -49.

Can you help Sammy find out the product of the odd factors of 49?

Factors of 49 are 1, 7, 49.
Odd factors of 49 are 1, 7, 49.
Hence product of odd factors of 49 is; 1 x 7 x 49 = 343.

Joey wants to write all the prime factors of 49 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 49 are 7, 7.
So in exponential form it can be written as 72.

How many factors are there for 49?

Factors of 49 are 1, 7, 49.
So there are in total 3 factors.

Kevin has been asked to write 2 factor(s) of 49. Can you predict the answer?

2 factor(s) of 49 are 1, 7.

Sammy is puzzled while calculating the prime factors of 49. Can you help him find them?

Factors of 49 are 1, 7, 49.
Prime factors of 49 are 7, 7

What is prime factorization of 49?

Prime factorization of 49 is 7 x 7 = 72.