Question

Which among the following pairs of numbers have the same number of factors?

• A. $16,81$
• B. $2,10$
• C. $3,9$
• D. $16,20$

Answer 1

The correct option is A

$16,81$

16, 81: $16=2\times 2\times 2\times 2$ and $81=3\times 3\times 3\times 3$, and thus both have exactly 4+1 = 5 factors.
2, 10: 2 has exactly two factors being a prime number, and 10, being a product of two distinct primes , 2 and 5 has exactly four factors.(1+1)(1+1)
3, 9: 3, being a prime has exactly two factors, and 9, being the square of a prime (3 x 3), has exactly three factors. (2+1)
16, 20: $16=2\times 2\times 2\times 2$ has 4+1 = 5 factors, and $20=2\times 2\times 5$ has $(2+1)(1+1)=6$ factors.