What is the number of factors of 24³ - 16³ - 8³?
33
Let the expression be A = 24³ - 16³ - 8³. We can factor this using the identity a³ - b³ - c³ = 3abc if a = b + c. Let a = 24, b = 16, c = 8. Note that 16 + 8 = 24, so a = b + c. Therefore, A = 3 * 16 * 8 * 24 = 9216. Now we find the prime factorization of 9216: 9216 = 2¹⁰ * 3². The number of factors is (10 + 1)(2 + 1) = 11 * 3 = 33.
Important Questions from Divisibility and Remainder
What is the sum of the digits of the least number which when divided by 12, 16 and 20 leaves the same remainder 6 in each case and it is divisible by 9?
As nine-digit number 89563x87y is divisible by 72. What is the value of \(\sqrt{7x-3y}\) ?
The greatest number that on dividing 2675 and 2320 leaves the reminder 5 and 6 ,respectively is :
Find the greatest number that exactly divides 2880, 6525 and 8307.
If a 10 - digit number 643x1145y2 is divisible by 88, then the value of (2x - 3y) for the largest value of y is :
