What is the Greatest Common Factor of 34575 and 34590?

Greatest common factor (GCF) of 34575 and 34590 is 15.

GCF(34575,34590) = 15

We will now calculate the prime factors of 34575 and 34590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34575 and 34590.

How to find the GCF of 34575 and 34590?

We will first find the prime factorization of 34575 and 34590. After we will calculate the factors of 34575 and 34590 and find the biggest common factor number .

Step-1: Prime Factorization of 34575

Prime factors of 34575 are 3, 5, 461. Prime factorization of 34575 in exponential form is:

34575 = 3¹ × 5² × 461¹

Step-2: Prime Factorization of 34590

Prime factors of 34590 are 2, 3, 5, 1153. Prime factorization of 34590 in exponential form is:

34590 = 2¹ × 3¹ × 5¹ × 1153¹

Step-3: Factors of 34575

List of positive integer factors of 34575 that divides 34575 without a remainder.

1, 3, 5, 15, 25, 75, 461, 1383, 2305, 6915, 11525

Step-4: Factors of 34590

List of positive integer factors of 34590 that divides 34575 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1153, 2306, 3459, 5765, 6918, 11530, 17295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34575 and 34590. The biggest common factor number is the GCF number.
So the greatest common factor 34575 and 34590 is 15.

Also check out the Least Common Multiple of 34575 and 34590