What is the Greatest Common Factor of 55762 and 55776?

Greatest common factor (GCF) of 55762 and 55776 is 14.

GCF(55762,55776) = 14

We will now calculate the prime factors of 55762 and 55776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 55762 and 55776.

How to find the GCF of 55762 and 55776?

We will first find the prime factorization of 55762 and 55776. After we will calculate the factors of 55762 and 55776 and find the biggest common factor number .

Step-1: Prime Factorization of 55762

Prime factors of 55762 are 2, 7, 569. Prime factorization of 55762 in exponential form is:

55762 = 2¹ × 7² × 569¹

Step-2: Prime Factorization of 55776

Prime factors of 55776 are 2, 3, 7, 83. Prime factorization of 55776 in exponential form is:

55776 = 2⁵ × 3¹ × 7¹ × 83¹

Step-3: Factors of 55762

List of positive integer factors of 55762 that divides 55762 without a remainder.

1, 2, 7, 14, 49, 98, 569, 1138, 3983, 7966, 27881

Step-4: Factors of 55776

List of positive integer factors of 55776 that divides 55762 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 83, 84, 96, 112, 166, 168, 224, 249, 332, 336, 498, 581, 664, 672, 996, 1162, 1328, 1743, 1992, 2324, 2656, 3486, 3984, 4648, 6972, 7968, 9296, 13944, 18592, 27888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 55762 and 55776. The biggest common factor number is the GCF number.
So the greatest common factor 55762 and 55776 is 14.

Also check out the Least Common Multiple of 55762 and 55776