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Guichard-Combinatorics-Graph-Theory
· Problem 1.2.1
Fundamentals
Mathematics — Probability · counting-factors
Problem
How many positive factors does
2
⋅
3
4
⋅
7
3
⋅
11
2
⋅
47
5
2 \cdot 3^4 \cdot 7^3 \cdot 11^2 \cdot 47^5
2
⋅
3
4
⋅
7
3
⋅
1
1
2
⋅
4
7
5
have? How many does
p
1
e
1
p
2
e
2
⋯
p
n
e
n
p_1^{e_1} p_2^{e_2} \cdots p_n^{e_n}
p
1
e
1
p
2
e
2
⋯
p
n
e
n
have, where the
p
i
p_i
p
i
are distinct primes?
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