When a certain number divides 67,82,97, they all leave a remainder of 7. Find the largest possible value of the number.

Question

asnaseer · Answer

lets call the unknown number x. then you can write this as:$$67=ax+7$$$$82=bx+7$$$$97=cx+7$$giving us:$$ax=60, bx=75, cx=90$$where a, b and c are some other unknown integers.
so now you just need to find the GCd (Greatest Common Divisor) of 60, 75 and 90

anonymous · Answer

so confusing?

asnaseer · Answer

which part do you find difficult to understand?

anonymous · Answer

OOO nvm

anonymous · Answer

i get it

asnaseer · Answer

ok - good

asnaseer · Answer

do you know how to find GCD of the 3 numbers?

anonymous · Answer

No

asnaseer · Answer

write them out as a product of their primes factors - that should help

anonymous · Answer

15?

asnaseer · Answer

$$60=2^2*3*5$$$$75=3*5^2$$$$90=2*3^2*5$$

asnaseer · Answer

then try and spot what is COMMON between all of them

asnaseer · Answer

e.g. 2 is not comon as it is not a factor of 75

asnaseer · Answer

3 IS common - can you spot another common factor?

anonymous · Answer

5?

asnaseer · Answer

good - so 3 and 5 are the only common factors.
so the answer is x=3*5=15

anonymous · Answer

thank you

asnaseer · Answer

yw