What is the Greatest Common Factor of 34758 and 34776?

Greatest common factor (GCF) of 34758 and 34776 is 18.

GCF(34758,34776) = 18

We will now calculate the prime factors of 34758 and 34776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34758 and 34776.

How to find the GCF of 34758 and 34776?

We will first find the prime factorization of 34758 and 34776. After we will calculate the factors of 34758 and 34776 and find the biggest common factor number .

Step-1: Prime Factorization of 34758

Prime factors of 34758 are 2, 3, 1931. Prime factorization of 34758 in exponential form is:

34758 = 2¹ × 3² × 1931¹

Step-2: Prime Factorization of 34776

Prime factors of 34776 are 2, 3, 7, 23. Prime factorization of 34776 in exponential form is:

34776 = 2³ × 3³ × 7¹ × 23¹

Step-3: Factors of 34758

List of positive integer factors of 34758 that divides 34758 without a remainder.

1, 2, 3, 6, 9, 18, 1931, 3862, 5793, 11586, 17379

Step-4: Factors of 34776

List of positive integer factors of 34776 that divides 34758 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 23, 24, 27, 28, 36, 42, 46, 54, 56, 63, 69, 72, 84, 92, 108, 126, 138, 161, 168, 184, 189, 207, 216, 252, 276, 322, 378, 414, 483, 504, 552, 621, 644, 756, 828, 966, 1242, 1288, 1449, 1512, 1656, 1932, 2484, 2898, 3864, 4347, 4968, 5796, 8694, 11592, 17388

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34758 and 34776. The biggest common factor number is the GCF number.
So the greatest common factor 34758 and 34776 is 18.

Also check out the Least Common Multiple of 34758 and 34776