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

 Apr 19, 2022
 #1
avatar+115 
-2

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.

 

sincerely▄︻デ✞☬🇮‌🇫‌1️⃣🇳‌1️⃣🇹‌¥☬✞══━一

 Apr 19, 2022
 #2
avatar+4 
+1

Fix ittttt

DarkProdigy  Apr 19, 2022
 #3
avatar+9459 
+1

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.

 Apr 19, 2022
edited by MaxWong  Apr 19, 2022

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