The product of all factors of n is 2,176,782,336,000,000,000,000,000,000,000,000
Find n.
If I told you 612=2,176,782,336 you shouldn't need a calculator.
product = 6^12 * 10^24
= 3^12 * 5^24 * 2^36
The first number I tried turned out to be the solution,
namely 3^1 * 5^2 * 2^3 = 600
This has (1+1)*(2+1)*(3+1) = 2*3*4 = 24 factors
Consider the prime factorization of these 24 factors.
12 factors feature 3^0 and 12 feature 3^1, so their product features 3^12
8 feature 5^0 and 8 feature 5^1 and 8 feature 5^2, so their product features 5^24
And 6 each feature 2^0 and 2^1 and 2^2 and 2^3 respectively, so their product features 2^36.
Final answer: 600
Edited on May 10, 2023, 3:02 pm
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