What is the Greatest Common Factor of 34845 and 34860?

Greatest common factor (GCF) of 34845 and 34860 is 15.

GCF(34845,34860) = 15

We will now calculate the prime factors of 34845 and 34860, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34845 and 34860.

How to find the GCF of 34845 and 34860?

We will first find the prime factorization of 34845 and 34860. After we will calculate the factors of 34845 and 34860 and find the biggest common factor number .

Step-1: Prime Factorization of 34845

Prime factors of 34845 are 3, 5, 23, 101. Prime factorization of 34845 in exponential form is:

34845 = 3¹ × 5¹ × 23¹ × 101¹

Step-2: Prime Factorization of 34860

Prime factors of 34860 are 2, 3, 5, 7, 83. Prime factorization of 34860 in exponential form is:

34860 = 2² × 3¹ × 5¹ × 7¹ × 83¹

Step-3: Factors of 34845

List of positive integer factors of 34845 that divides 34845 without a remainder.

1, 3, 5, 15, 23, 69, 101, 115, 303, 345, 505, 1515, 2323, 6969, 11615

Step-4: Factors of 34860

List of positive integer factors of 34860 that divides 34845 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 83, 84, 105, 140, 166, 210, 249, 332, 415, 420, 498, 581, 830, 996, 1162, 1245, 1660, 1743, 2324, 2490, 2905, 3486, 4980, 5810, 6972, 8715, 11620, 17430

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34845 and 34860. The biggest common factor number is the GCF number.
So the greatest common factor 34845 and 34860 is 15.

Also check out the Least Common Multiple of 34845 and 34860