SOLUTION: I am a natural number. I am divisible by 7. I am less than 120. My GCD with 120 is 15. Who am I?

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: I am a natural number. I am divisible by 7. I am less than 120. My GCD with 120 is 15. Who am I?       Log On


   

Question 1149250: I am a natural number.
I am divisible by 7.
I am less than 120.
My GCD with 120 is 15.
Who am I?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Because the number is divisible by 7, 7 is one of the prime factors of the number.

(2) Because the GCD of the number and some other number is 15, 3 and 5 are prime factors of the number.

So the number has prime factors of 3, 5, and 7, making the number 3*5*7*k where k is some integer. But 3*5*7 = 105; since the number is less than 120, it must be 105.