Ques 9 Number theory quiz II

#1

1366×768 105 KB

#2

I believe there are 3.
They are : 2,120 , 6,40, 10,24

In order to find the number of pairs with a given GCD and LCM, find the number n of prime factors in LCMGCD. The number of pairs is equal to 2n.

Example: GCD=2 and LCM=120
LCM/GCD=60=2power2∗5∗3
therefore we have 2power3 (we have 3 prime factors) pairs.

#3

Answer is 8 not 3, What are these pairs?

#4

I guess the answer should be 8 only

image
image942×372 108 KB

And prime factor pairs are 3

#5

ok…