What is the number of factors of 24^{3}-16^{3}-8^{3}?

Explanation

Using the algebraic identity (a+b)^3 - a^3 - b^3 = 3ab(a+b), where a=16 and b=8, we have 24^3 - 16^3 - 8^3 = 3 \times 16 \times 8 \times 24 = 3 \times 2^4 \times 2^3 \times (2^3 \times 3) = 3^2 \times 2^{10}. The number of factors is (2+1)(10+1) = 3 \times 11 = 33.

Related questions on Arithmetic

• What is the remainder when (17^{25} + 19^{25}) is divided by 18?
• A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what rat...
• Let P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the numbe...
• Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X an...
• Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number...