# Factors of 196

Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196

#### How to find factors of a number

 1.   Find factors of 196 using Division Method 2.   Find factors of 196 using Prime Factorization 3.   Find factors of 196 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 196

• Divide 196 by 1: 196 ÷ 1 : Remainder = 0
• Divide 196 by 2: 196 ÷ 2 : Remainder = 0
• Divide 196 by 4: 196 ÷ 4 : Remainder = 0
• Divide 196 by 7: 196 ÷ 7 : Remainder = 0
• Divide 196 by 14: 196 ÷ 14 : Remainder = 0
• Divide 196 by 28: 196 ÷ 28 : Remainder = 0
• Divide 196 by 49: 196 ÷ 49 : Remainder = 0
• Divide 196 by 98: 196 ÷ 98 : Remainder = 0
• Divide 196 by 196: 196 ÷ 196 : Remainder = 0

Hence, Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196

#### 2. Steps to find factors of 196 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 196 using the division method, follow these steps:

• Step 1. Start dividing 196 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 196, which is 2. Divide 196 by 2 to obtain the quotient (98).
196 ÷ 2 = 98
• Step 3. Repeat step 1 with the obtained quotient (98).
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 196 is, 196 = 2 x 2 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 196 as shown below:

So, the prime factorization of 196 is, 196 = 2 x 2 x 7 x 7.

#### 3. Find factors of 196 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 196 would be the two numbers which, when multiplied, give 196 as the result.

The following table represents the calculation of factors of 196 in pairs:

Factor Pair Pair Factorization
1 and 196 1 x 196 = 196
2 and 98 2 x 98 = 196
4 and 49 4 x 49 = 196
7 and 28 7 x 28 = 196
14 and 14 14 x 14 = 196

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 196. They are called negative pair factors.

Hence, the negative pairs of 196 would be ( -1 , -196 ) , ( -2 , -98 ) , ( -4 , -49 ) , ( -7 , -28 ) and ( -14 , -14 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 196 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 196.
• Every number is a factor of zero (0), since 196 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 7, 14, 28, 49, 98, 196 are exact divisors of 196.
• Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. Each factor divides 196 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 28, 49, 98, 196 are all less than or equal to 196.

• Which is the smallest prime factor of 196?

The smallest prime factor of 196 is 2.

• Is 196 a whole number?

Yes 196 is a whole number.

• What are the prime factors of 196?

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196.
Prime factors of 196 are 2, 2, 7, 7.

• What two numbers make 196?

Two numbers that make 196 are 2 and 98.

• What are multiples of 196?

First five multiples of 196 are 392, 588, 784, 980.

• What is the sum of all factors of 196?

The sum of all factors of 196 is 399.

• What are five multiples of 196?

First five multiples of 196 are 392, 588, 784, 980, 1176.

• Is 196 a perfect square?

Yes 196 is a perfect square.

• What is the greatest prime factors of 196?

The greatest prime factor of 196 is 7.

#### Examples of Factors

How many factors are there for 196?

Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196.
So there are in total 9 factors.

Kevin has been asked to write 8 factor(s) of 196. Can you predict the answer?

8 factor(s) of 196 are 1, 2, 4, 7, 14, 28, 49, 98.

Sammy is puzzled while calculating the prime factors of 196. Can you help him find them?

Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196.
Prime factors of 196 are 2, 2, 7, 7

What is prime factorization of 196?

Prime factorization of 196 is 2 x 2 x 7 x 7 = 22 x 72.

Ariel has been assigned the task to find the product of all the prime factors of 196. Can you help her?

Prime factors of 196 are 2, 2, 7, 7.
Hence, the product of prime factors of 14.

Can you help Rubel to find out the product of the even factors of 196?

Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196.
Even factors of 196 are 2, 4, 14, 28, 98, 196.
Hence, product of even factors of 196 is; 2 x 4 x 14 x 28 x 98 x 196 = 60236288.

Joy wants to calculate mean of all the factors of 196. Help him in finding the mean of 196.

Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 196 is 1 + 2 + 4 + 7 + 14 + 28 + 49 + 98 + 196 = 399.
Hence, the mean of factors of 196 is 399 ÷ 9 = 44.33.