Factors of 196

Hey kids! Do you know that when you multiply the number 14 to itself, you will get 196 as the answer? Yes, 196 is a perfect square number. In this lesson, let us learn about the prime factors of 196, pair factors of 196, prime factorization of 196, and the methods to find factors of 196.

• Factors of 196: 1, 2, 4, 7, 14, 14, 28, 49, 98, 196
• Prime Factorization of 196: 2² ×  7²  or 2 × 2 × 7 × 7

So, when we multiply any two whole numbers with each other and get 196 as the product, we can say that both the numbers are the factors of 196. 

Observe the following as seen in the rainbow above:

• 1 × 196 = 196 
• 2 × 98 = 196 
• 4 × 49 = 196 
• 7 × 28 = 196 
• 14 × 14 = 196 
• 196 ×  1 = 196 

Hence, the factors of 196 can be listed as 1, 2, 4, 7, 14, 28, 49, 98, and 196.

Explore factors using illustrations and interactive examples.

• Factors of 169: The factors of 169 are 1, 13, and 169.
• Factors of 225: The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
• Factors of 180:  The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36,  45, 60, 90, and 180.
• Factors of 90: The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
• Factors of 192: The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.

• We can use different methods to find factors of 196 such as the division method and the prime factorization method.
• In the division method, we see what numbers divide 196 exactly without a remainder and in prime factorization, we express 196 as a product of its prime factors..
• Factors of 196 are those numbers that divide it completely and give the remainder as 0. Find the numbers starting from 1, that exactly divide 196 using the known divisibility rules. 

• 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

The division shows that the number 196 is exactly divisible by 1, 2, 4, 7, 14, 28, 49, 98, and 196.

• The factors of 196 can be represented by the upside-down division method as:

Thus the prime factorization is 2 × 2 × 7 × 7 = 2 ²  × 7 ². Now that we have done the prime factorization of the number, we can multiply them and get the other factors. 

• The numbers which we multiply to get 196 are the factors of 196.
• The factors of 196 can be listed as 1, 2, 4, 7, 14, 28, 49, 98, and 196.
• The factor pairs of a number are the set of two numbers which, when multiplied together, give the original number.

What is the prime factorization of 196 using exponents?

The prime factorization of 196 is 196 = 2 × 2 × 7 × 7 and can be represented as 196 = 2 ² × 7 ² using exponents.

Is 81 a prime number or a composite number?

• A prime number does not have a factor other than 1 and itself.
• A composite number has factors other than 1 and itself.
• Factors of 81 are 1, 3, 9, 27, and 81. Hence, it is a composite number.

What is the prime factorization of 196?

The prime factorization of 196 is 196 = 2 × 2 × 7 × 7 = 2 ² × 7 ²

What is the greatest common factor (GCF) of 196 and 200?

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

The factors of 200  are 1, 2, 4, 5, 10, 20, 40, 50,100, and 200.

The GCF of 196 and 200 is 4.

What is the prime factorization of 198?

 The prime factorization of 198 = 2 × 3 × 3 × 11