**4** would be the sum of exponents of the prime factors in the prime factorization of 196. Thus, 4 is the sum of exponents of prime factors in the prime factorization of 196.

Prime factors are those prime numbers which constitute to the formation of a number by multiplication of smaller prime numbers. Hence, the sum of exponents of prime factors in the prime factorization of 250 = 4. If α and β are zeroes of the polynomial 2x²-5x+7 , then find the value of 1/α + 1/β.

What are the prime factors of 196? The prime factorisation of 196 is 2 × 2 × 7 × 7 Or 2^2 × 7^2 and the prime factors of 196 are 2 and 7.

To add exponents, both the exponents and variables should be alike. You add the coefficients of the variables leaving the exponents unchanged. Only terms that have same variables and powers are added. This rule agrees with the multiplication and division of exponents as well.

The exponent of any prime in a factorial is given by, e1 = [n/p1] + [n/p12] + [n/p13] … Here, [.] is the greatest integer function.

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 72, 90, 120, 180, 360. By adding up all the factors of 360, the sum will be 1170.

The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. So, the sum of factors of 144 is 403.

We know that the exponent of a number a^{m} is m. The sum of the exponents of prime factors in the prime factorization of 98 is 3.

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240. So, the sum of factors of 240 is 744.

The sum of all the factors of 36 can be calculated by adding 1, 2, 3, 4, 6, 9, 12, 18, 36 which is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91.

Square Root of 196 By Prime Factorization Method

- Prime factorization of 196: 2
^{2}× 7^{2} - Prime factors of 196 in pairs: (2 × 2) × (7 × 7)
- Now square root of 196: √196 = √(2 × 2) × (7 × 7) √196 = √(2 × 7)
^{2}√196 = (2 × 7) = 14.

Solution: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 therefore sum of the factors is 1+ 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96 = 252.

Prime factorization of 130 is 2 × 5 × 13. Step-by-step explanation: If we put all of it together we have the factors 2 x 5 x 13 = 130. It can also be written in exponential form as 21 x 51 x 131.

Factors of 456 are numbers that, when multiplied in pairs give the product as 456. It has total 16 factors of which 456 is the biggest factor and the prime factors of 456 are 2, 3, 19. The sum of all factors of 456 is 1200.

Answer: 324 is a composite number. The exponents in the prime factorization are 2 and 4. Adding one to each and multiplying we get (2 + 1)(4 + 1) = 3 x 5 = 15.

The sum of all factors of 325 is 434 and its factors in Pairs are (1, 325), (5, 65), (13, 25).

The sum of all the factors of 120 can be calculated by adding 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 which is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40+ 60 + 120 = 360.

Sum of the powers = 8 + 4 = 12.

Factors of 420 = 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Therefore, sum of factors of 420 are 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 28 + 30 + 35 + 42 + 60 + 70 + 84 + 105 + 140 + 210 + 420 = 1344.

Answer and Explanation: The prime factorization of 100 is 2 * 2 * 5 * 5. Using exponents, this number can also be written as 2^2 * 5^2.

Therefore, the exponent of 2 in the prime factorization of 144 is 4.

The correct Answer is 196 is not a perfect cube.