What is the Greatest Common Factor of 34748 and 34762?

Greatest common factor (GCF) of 34748 and 34762 is 14.

GCF(34748,34762) = 14

We will now calculate the prime factors of 34748 and 34762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34748 and 34762.

How to find the GCF of 34748 and 34762?

We will first find the prime factorization of 34748 and 34762. After we will calculate the factors of 34748 and 34762 and find the biggest common factor number .

Step-1: Prime Factorization of 34748

Prime factors of 34748 are 2, 7, 17, 73. Prime factorization of 34748 in exponential form is:

34748 = 2² × 7¹ × 17¹ × 73¹

Step-2: Prime Factorization of 34762

Prime factors of 34762 are 2, 7, 13, 191. Prime factorization of 34762 in exponential form is:

34762 = 2¹ × 7¹ × 13¹ × 191¹

Step-3: Factors of 34748

List of positive integer factors of 34748 that divides 34748 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 68, 73, 119, 146, 238, 292, 476, 511, 1022, 1241, 2044, 2482, 4964, 8687, 17374

Step-4: Factors of 34762

List of positive integer factors of 34762 that divides 34748 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 191, 382, 1337, 2483, 2674, 4966, 17381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34748 and 34762. The biggest common factor number is the GCF number.
So the greatest common factor 34748 and 34762 is 14.

Also check out the Least Common Multiple of 34748 and 34762