Number of Even Factors

Number Theory Level 3

How many even factors does ( 4 6 ) (4^{6}) ( 3 6 2 ) (36^{2}) have?


The answer is 80.

Dan Shin by Dan Shin , 21, USA

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1 solution

( 4 6 ) ( 3 6 2 ) = ( 2 16 ) ( 3 4 ) (4^{6})(36^{2}) = (2^{16})(3^{4}) The number of even factors is simply the total number of factors minus the number of odd factors, which is: 17 ∗ 5 − 5 = 80 17*5-5=80

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Great solution! You can also find the even factors by fixing a 2. In this case, you can rewrite the equation as 2 ⋅ 2 15 ⋅ 3 4 2 \cdot 2^{15} \cdot 3^4 and then just find the number of factors of 2 15 ⋅ 3 4 2^{15} \cdot 3^4 .

Arulx Z - 5 years, 4 months ago

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