Cool Factor Trick

How many factors does 6 10 5 100 7 7 6 h a v e ? 6^{10} * 5^{100} * 77^{6} have?


The answer is 598829.

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2 solutions

Li Yuelin
May 10, 2015

Firstly we factorize the number into prime numbers, so we obtain 2^10×3^10×5^100×7^6×11^6. For each prime, we can find out how many ways there are to decide its power. For example, 2 can have 11 different powers (2^0, 2^1, ... 2^10). So for each prime, the number of ways to decide its power is equal to n+1, where n is the power of that prime in the prime factorization. So we multiply the number of ways to decide each power of a prime number, and get 11×11×101×7×7 = 598829

Great explanation, Li Yuelin! Exactly what I was thinking, good job!

Jonathan Hsu - 6 years, 1 month ago
Ashwin Padaki
May 11, 2015

Follow-up: What is the sum of factors of that number?

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