What is the Greatest Common Factor of 34874 and 34888?

Greatest common factor (GCF) of 34874 and 34888 is 14.

GCF(34874,34888) = 14

We will now calculate the prime factors of 34874 and 34888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34874 and 34888.

How to find the GCF of 34874 and 34888?

We will first find the prime factorization of 34874 and 34888. After we will calculate the factors of 34874 and 34888 and find the biggest common factor number .

Step-1: Prime Factorization of 34874

Prime factors of 34874 are 2, 7, 47, 53. Prime factorization of 34874 in exponential form is:

34874 = 2¹ × 7¹ × 47¹ × 53¹

Step-2: Prime Factorization of 34888

Prime factors of 34888 are 2, 7, 89. Prime factorization of 34888 in exponential form is:

34888 = 2³ × 7² × 89¹

Step-3: Factors of 34874

List of positive integer factors of 34874 that divides 34874 without a remainder.

1, 2, 7, 14, 47, 53, 94, 106, 329, 371, 658, 742, 2491, 4982, 17437

Step-4: Factors of 34888

List of positive integer factors of 34888 that divides 34874 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 89, 98, 178, 196, 356, 392, 623, 712, 1246, 2492, 4361, 4984, 8722, 17444

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34874 and 34888. The biggest common factor number is the GCF number.
So the greatest common factor 34874 and 34888 is 14.

Also check out the Least Common Multiple of 34874 and 34888