  # The sum of the exponents of the prime factors in the prime factorisation of 196, is

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Updated on: September 25th, 2023 The sum of the exponents of the prime factors in the prime factorisation of 196 is 4. When a number is expressed as the product of its prime factors, it is known as prime factorization. A number is considered to be prime if it only has two factors that are 1 and the number itself.

Following is the step by step process to determine the prime factors in the prime factorisation of 196:

196 = 2 × 2 × 7 × 7

196 = 22 × 72

In 22 × 72 the exponents of both 2 and 7 are 2 Therefore the sum of exponents will be 2 + 2 = 4.

Table of content ## Sum of Exponents of Prime Factors in Prime Factorisation of 196

To find the sum of exponents of prime factors in the prime factorisation of any number, candidates should have an idea of what the terms prime factors, prime factorisation and exponents. Let us have a look at the definitions of these terms and understand what they are.

• Prime Factors: A natural number other than 1 with only the number 1 and itself as factors is known as a prime factor. Actually, 2, 3, 5, 7, 11, 13, 17, and so on are the first few prime numbers.
• Prime Factorization: The process of expressing a number as the multiple of prime numbers is known as prime factorization.
• Exponent: Exponent is a mathematical operation that involves the base and the power. The power of a number is called its exponent.

Summary:

## The sum of the exponents of the prime factors in the prime factorisation of 196, is

In the prime factorisation of 196, the sum of the exponents of the prime factors is 4. Prime factorization is the process of expressing a number as the product of its prime factors. A number is deemed prime if it has just two factors: 1 and the number itself.

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