Question

18.. Find the total number of different divisors contained in the number 2640
1) 40
2) 38
3) 7
4)5​

Answer 1

1) 40

Factors of 2640 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 33, 40, 44, 48, 55, 60, 66, 80, 88, 110, 120, 132, 165, 176, 220, 240, 264, 330, 440, 528, 660, 880, 1320, 2640.

Answer 2

Answer:

The total no. of divisors of 2640 are 40.

Step-by-step explanation:

Number of divisors of a number:

• Let n be the given number.

• Do prime factorization of n, take all the exponents in the factorization, add 1 to each, and then multiply these(exponents+1) together then we get the no. of divisors of the number n.
• Suppose n = pᵃqᵇrˣ

          where  p,q,r are the prime factors and a,b,x are the powers.

• The number of divisors of n =(a+1)(b+1)(x+1)

Given number is 2640.

    Write the number 2640 into prime factors

      2640 = 2×2×2×3×11×2×5

                = 2×2×2×2×3×5×11  

                = 2⁴×3×5×11

    The total no. of divisors = (4+1)(1+1)(1+1)(1+1)

                                            = 5×2×2×2

                                            = 40

   Hence, the total no. of divisors of 2640 are 40.

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