Factors of 196 using Prime Factorization
The Factors of 196
What are the Factors of 196?
Integers that divide 196 without leaving any remainder are known as the factors of 196.
For example, 7 is a factor of 196 because when we divide 196 by 7, it leaves 28 as the quotient and 0 as the remainder. Here, the quotient is also a factor of 196.
So, to check if the number is a factor of 196 or not, divide 196 by that number and verify whether the remainder is zero or not.
Factor List of 196
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
The Prime Factors of 196
The number 196 is a composite number, that is, it has more than two numbers as factors. To find the prime factors, first we will divide the number 196 by its smallest prime factor, that is, 2.
196 ÷ 2 = 98
Again, divide by 2;
98 ÷ 2 = 49
49 ÷ 2 = 24.5, which is not a factor.
Now, proceed with the next prime numbers, which are 3, 5, and 7.
49 ÷ 3 = 16.33, not a factor
49 ÷ 5 = 9.8, not a factor
49 ÷ 7 = 7
Again, divide by 7;
7 ÷ 7 = 1
So, the prime factorization of 196 = 2 × 2 × 7 × 7 or 2\( ^2 \) × 7\( ^2 \).
This means that 2 and 7 are the prime numbers of 196.
The Factor Pairs of 196
The factor pairs are two factors that, when multiplied together ,give the original number as the result.
Example: (7, 28) is the factor pair of 196.
The factor pairs can be a positive pair or a negative pair.
The Positive Factor Pairs of 196
When two positive numbers are multiplied, the product is positive.
Hence, the positive pair factors of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).
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Rapid Recall
The factors of 196 are:
Solved Factors of 196 Examples
Example 1: Find the common factor of 196 and 144.
Solution:
The factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, and 196
The factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
Therefore, the common factors of 196 and 144 are 1, 2, and 4.
Example 2: Find the common factors of 196 and 201.
Solution:
The factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, and 196
The factors of 201 = 1, 3, 67, and 201
Therefore, the common factor of 196 and 201 is 1.
Example 3: Find the common factors of 64 and 196.
Solution:
The factors of 64 = 1, 2, 4, 8, 16, 32, and 64
The factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, and 196
Therefore, the common factors of 64 and 196 are 1, 2, and 4
Example 4: Sarah has 196 different stamps in her collection. Can she stick them in a notebook such that there are 7 stamps on each page and no stamps are left out?
Solution:
To find out if 196 stamps can be grouped in the groups of 7, let us look at the factors of 196.
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196
We can see that 7 is a factor of 196. This suggests that we can divide 196 stamps into groups of 7.
Therefore, Sarah can stick 7 stamps on one page and no stamps will be left out.
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
So, the smallest factor of 196 is 1, and the greatest factor is 196 itself.
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196
Sum of factors = 1 + 2 + 4 + 7 + 14 + 28 + 49 + 98 + 196 = 399
So, the sum of factors of 196 is 399.
Yes, 14 is a factor of 196. This is because when the number 14 divides 196, it leaves 14 as the quotient and 0 as the remainder.
The prime factorization of 196 is 2 × 2 × 7 × 7 or 2\( ^2 \) × 7\( ^2 \).
The positive factor pairs of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).