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How many positive integers divide evenly into either 144 or 196 but not 72?

Guest Apr 19, 2022

Kakashi · Answer 1 · 2022-04-19T02:39:24

1 - 144 mod 16==0, 144 mod 48==0, 144 mod 144==0. None of these numbers divides 72 evenly.

2 - 196 mod 7==0, 196 mod 14==0, 196 mod 28==0, 196 mod 49==0, 196 mod 98==0 and 196 mod 196==0. None of these numbers divides 72 evenly.

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MaxWong · Answer 2 · 2022-04-19T06:18:55

Note that it is not possible to divide evenly into 144 but not 72, since 144 = 72 • 2.

Factors of 196: 1, 2, 7, 14, 28, 98, 196

We see that 7, 14, 28, 98, and 196 divide evenly into 196, but not 72, since 72 is not divisible by 7.

The answer is obvious now.