July 17, 2024

Prime Factors and Pair Factors of 196

Factors of 196

What are the Factors of 196?

In mathematics, a factor of a number is a number that divides the given number. As a result, a factor is simply a divisor of the given integer. We can use both the multiplication and division methods to get the factors.

How to Find the Factors of 196?

Factors of 196  by Multiplication: To find the factors using the multiplication, write the given number as the product of two numbers in different possible ways. All the numbers that we are using  in  these products are the factors of the given number.

Since 196= 1 x 196

196=2 x 98

196= 4 x 49

196= 7 x 28

196= 14 x 14

Thus , the factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, and 196.

Factors of 196 by division:

Since factors are the exact divisors of the numbers, So we can  find the factors  of  196 by dividing 196  by numbers less than and equal to 196 .

196 ÷ 1 = 196

196 ÷ 2 = 98

196 ÷ 4 = 49

196 ÷ 7 = 28

196 ÷ 14 = 14

196 ÷ 28 = 7

196 ÷ 49 = 4

196 ÷ 98 = 2

196 ÷ 196 = 1

We can see that in each case remainder is zero .Therefore, factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, and 196.

Factor of 196 in Pairs

The factors of any number can be both positive and negative. The following table represents the positive factor pairs and negative factor pairs of  196.

 Positive factor pairs of 160 Negative factor pairs of 160 196=196  x 1 196=(-196)  x(- 1) 196= 2 x 98 196= (-2) x(- 98) 196= 4 x 49 196= (-4 )x(- 49) 196=  14 x 14 196= (-14) x (-14) 196= 7 x 28 196=(-7) x (-28)

Therefore, the positive pair factors of 196 are (1, 196), (2, 98), (4, 49), (7, 28), (14, 14).

Also, the negative pair factors of 196 are (-1, -196), (-2, -98), (-4, -49), (-7, -28), (-14, -14).

Prime factors of 196

How to calculate Prime Factors of 196?

Expressing a  given number as the product of prime numbers is called the prime factorization of the given numbers.

Prime factorization of 196 by division method:

To find the prime factors of an integer using the division method, follow the steps below:

step 1 : Take the smallest prime number which  completely divide the given number.

Step 2:  Again, divide the quotient by the smallest prime number.

Step 3: Continue until the quotient is equal to one.

Step 4: Finally, multiply all the prime factors.

Prime factorization of 196 by  factor tree method:

To find the prime factorization of 196 by factor tree method, the following steps should be followed:

Step 1: Find the least prime number by which the given number is divisible. Resolve the number into two factors taking this prime number as one of them.

Step 2: Resolve the second factor further into two factors out of which at least one factor is prime.

Step 3: Go on splitting the factors till you get all the prime factors.

Step 4: Circle all the prime factors.

The prime factorisation of 196 is 2 × 2 × 7 × 7  or $2^{2}&space;\times&space;7^{2}$  and the prime factors of 196 are 2 and 7.

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