Factors Of 196

We can tell if a number has more than 2 factors just by seeing if a number is a prime number or not. As none of the even numbers except 2 are prime numbers, we can tell that 196 has more than 2 factors. Let us find what the factors are.

Negative factors of 196:  -1, -2, -4, -7, -14, -28, -49, -98, and -196

Prime factors of 196: The prime factors of 196 are 2 and 7.

Prime factorization of 196: 2 × 2 × 7 × 7. 

The sum of factors of 196: 1+2+4+7+14+28+49+98+196= 399.
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 196.

• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization
   

In the multiplication method, we find pairs of numbers where the product will be 196. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 196.

Step 2: These numbers will be called the factors of 196.

Step 3: Students have to write these pairs of numbers for this method.

List of numbers whose product is 196

196×1= 196

98×2= 196

49×4= 196

28×7= 196

14×14= 196

So the pair of numbers whose product is 196 are (1,196), (98,2), (49,4), (28,7), and (14,14).
 

For the division method, the process of division will go on until the remainder becomes zero.

Step 1: For the division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 196÷1 = 196.

Step 2: Then check with the next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 196÷2= 98 and so on.

Prime factorization is the process where the number will be a product of prime factors or prime numbers.

Prime Factors Of 196:The prime factors of 196 are 2 and 7. We find the prime factors of 196 by two ways.

• Prime Factorization

• Factor Tree

By Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 196, the steps are like this:

196/2= 98

98/2= 49

49/7= 7

7/7= 1

As 7 is a prime number, it is only divisible by 7. Hence, The prime factorization of the number 196 is 2×2×7×7.
 

This is a very easy method because in many ways it’s almost the same as a prime factorization. We will break down huge numbers in this case to get what we call a factor tree.

Step 1: 196 divided by 2 gives us the answer being 98.

Step 2: 98 divided by 2 gives us 49.

Step 3: 49 divided by 7 gives us 7.

Step 4: 7 divided by 7 gives us 1.

Step 5: This can’t be divided any further.

There are positive and negative factor pairs for a given number. Let us look at these factor pairs.

Positive Factor Pairs: (1,196), (98,2), (49,4), (28,7)  and (14,14).

Negative Factor Pairs: (-1,-196), (-98,-2), (-49,-4), (-28,-7)  and (-14,-14).
 

• Factors: Numbers that can be multiplied together to produce another number without leaving a remainder. For example, 1 and 196 are factors of 196.

• Composite Number: A natural number greater than 1 that has more than two factors. For example, 196 is composite since it has multiple factors.

• Multiplication Method: A way to find numbers with which the original number can be multiplied to give the product.

• Divisibility: The ability to divide one number into the other without having a remainder. In example, you can observe 196 is divisible by 2