Divisors

[Gabry00]

hello, i'm Gabry00, i need a basic math information, that i can't find in any book or forum, i need the max divisor of 36380 and 99360, it's for a math problem, i hope someone answers, byee

 

[MathLover1]

The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b).

first find prime factors
36380 = 2^2×5×17×107 (5 prime factors, 4 distinct)
99360 = 2^5×3^3×5×23 (10 prime factors, 4 distinct)

you can rewrite primes of 99360 as
99360 = 2^2*2^3×3^3×5×23

now compare them and find common factors in both given numbers
36380 = 2^2×5×17×107
99360 = 2^2*2^3×3^3×5×23

so, GCD=2^2×5=20

answer: gcd(36380, 99360) =20