The Factors of 196 are the numbers which get multiplied and produce the result as 196. Suppose multiplying 2 and 8, we get 16, i.e. 2 Ã— 8 = 16 such that 2 and 8 are the factors of 16. Also, (2, 8) is called one of the factor pairs of 16. Similarly, we can find the factors of the number 196. In this article, you will get the factors of 196, how to find the factors of a number 196 in pairs using different methods and prime factors of 196 with detailed steps.
What are the Factors of 196?
Also, we know that the factors of 196 are the exact divisors of that number. The number 196 is a composite number and hence it has more than two factors, that means it has factors other than 1 and 196.
Factors of 196 |
1, 2, 4, 7, 14, 28, 49, 98, and 196. |
However, we can find the factors for any given number in two ways, namely division method and factor pair method.
How to Find the Factors of 196?
Go through the steps given below to understand the process of finding the factors of 196.
Step 1: First, write the number 196 in your notebook.
Step 2: Find the two numbers, which on multiplication gives 196, suppose 2 and 98, such as 2 Ã— 98 = 196.
Step 3: We know that 2 is a prime number which has only two factors, i.e. 1 and the number itself. So, we cannot factorize it further.
2 = 1 Ã— 2
Step 4: Now, letâ€™s try with different combinations of numbers in multiplication that produce the result as 196, such as
4 Ã— 49 = 196
7 Ã— 28 = 196
14 Ã— 14 = 196
Step 5: Therefore, factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, and 196.
Factors of 196 by Division Method
As we know, factors are the exact divisors of the numbers. So we can also find the factors for the 196 by division method.
196 Ã· 1 = 196 {remainder = 0, 1 and 196 are factors}
196 Ã· 2 = 98 {remainder = 0, 2 and 98 are factors}
196 Ã· 4 = 49 {remainder = 0, 4 and 49 are factors}
196 Ã· 7 = 28 {remainder = 0, 7 and 28 are factors}
196 Ã· 14 = 14 {remainder = 0, 14 is a factor}
Factor of 196 in Pairs
The factors of any number can be both positive and negative. To get the pair factors of 196, multiply the 2 numbers in a pair to have the original number as 196. Such numbers are tabulated below:
Positive Factor Pairs |
Negative Factor Pairs |
1 Ã— 196 = 196; (1, 196) |
(-1) Ã— (-196) = 196; (-1, -196) |
2 Ã— 98 = 196; (2, 98) |
(-2) Ã— (-98) = 196; (-2, -98) |
4 Ã— 49 = 196; (4, 49) |
(-4) Ã— (-49) = 196; (-4, -49) |
7 Ã— 28 = 196; (7, 28) |
(-7) Ã— (-28) = 196; (-7, -28) |
14 Ã— 14 = 196; (14, 14) |
(-14) Ã— (-14) = 196; (-14, -14) |
28 Ã— 7 = 196; (28, 7) |
(-28) Ã— (-7) = 196; (-28, -7) |
49 Ã— 4 = 196; (49, 4) |
(-49) Ã— (-4) = 196; (-49, -4) |
98 Ã— 2 = 196; (98, 2) |
(-98) Ã— (-2) = 196; (-98, -2) |
196 Ã— 1 = 196; (196, 1) |
(-196) Ã— (-1) = 196; (-196, -1) |
Therefore, the positive pair factors of 196 are (1, 196), (2, 98), (4, 49), (7, 28), (14, 14), (28,7), (49, 4), (98, 2), and (196, 1).
Also, the negative pair factors of 196 are (-1, -196), (-2, -98), (-4, -49), (-7, -28), (-14, -14), (-28, -7), (-49, -4), (-98, -2), and (-196, -1).
Below are the important facts about the factors of 196.
- The total number of factors of 196 is 9.
- 196 is a perfect square number.
- The sum of factors of 196 is 399.
- The number of even factors of 196 is 6.
- The odd factors of 196 are 1, 7, and 49.
How to calculate Prime Factors of 196?
By prime factorization method, we can write the prime factors of 196 as given below.
Step 1: The first step is to divide the number 196 with the smallest prime number, i.e. 2.
196 Ã· 2 = 98
2 is a prime factor of 196
Step 2: Now, we divide 98 by 2.
98 Ã· 2 = 49; again 2 is a prime factor.
Step 3: Divide 49 by 2.
49 Ã· 2 = 24.5
As we know, the factors cannot be a fraction, therefore, 2 is not the prime factor for 49.
Step 4: Now, proceed to the next prime numbers, i.e. 3, 5, 7 and so on.
49 Ã· 3 = 16.33
49 Ã· 4 = 12.25
49 Ã· 5 = 9.8
49 Ã· 6 = 8.1667
49 Ã· 7 = 7; 7 is one of the prime factors.
Step 5: Divide 7 as:
7 Ã· 2 = 3.5
7 Ã· 3 = 2.33
7 Ã· 5 = 1.4
7 Ã· 7 = 1
Finally, we received 1 in the above process. Hence, we cannot proceed with the division method.
Thus, the prime factorisation of 196 can be expressed as 2 Ã— 2 Ã— 7 Ã— 7.
Prime factorisation of 196 is: 2 Ã— 2 Ã— 7 Ã— 7 Or 2^{2} Ã— 7^{2} |
Prime factors of 196 are: 2 and 7 |
Note:
The exponents in the prime factorization of 196 are 2 and 2. By adding one to each and multiplying them we get, (2 + 1)(2 + 1) = 3 Ã— 3 = 9. Thus, 196 has exactly 9 factors.
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Frequently Asked Questions on Factors of 196
What are the factors of 196?
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
What are the prime factors of 196?
The prime factorisation of 196 is 2 Ã— 2 Ã— 7 Ã— 7 Or 2^2 Ã— 7^2 and the prime factors of 196 are 2 and 7.
What are the factors of 197?
The factors of 197 are 1 and 197 only, since it is a prime number.
What is the number of factors of 196?
The number of unique factors of 196 is 9 and they are 1, 2, 4, 7, 14, 28, 49, 98, 196.
How do you find the factors of 196?
The factors of a number 196 can be found by identifying the pair of numbers which get multiplied to produce 196. We can also find the factors of 196 by the division method, where the exact divisors are the factors of the number.