What is the Greatest Common Factor of 83762 and 83776?

Greatest common factor (GCF) of 83762 and 83776 is 14.

GCF(83762,83776) = 14

We will now calculate the prime factors of 83762 and 83776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83762 and 83776.

How to find the GCF of 83762 and 83776?

We will first find the prime factorization of 83762 and 83776. After we will calculate the factors of 83762 and 83776 and find the biggest common factor number .

Step-1: Prime Factorization of 83762

Prime factors of 83762 are 2, 7, 31, 193. Prime factorization of 83762 in exponential form is:

83762 = 2¹ × 7¹ × 31¹ × 193¹

Step-2: Prime Factorization of 83776

Prime factors of 83776 are 2, 7, 11, 17. Prime factorization of 83776 in exponential form is:

83776 = 2⁶ × 7¹ × 11¹ × 17¹

Step-3: Factors of 83762

List of positive integer factors of 83762 that divides 83762 without a remainder.

1, 2, 7, 14, 31, 62, 193, 217, 386, 434, 1351, 2702, 5983, 11966, 41881

Step-4: Factors of 83776

List of positive integer factors of 83776 that divides 83762 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 17, 22, 28, 32, 34, 44, 56, 64, 68, 77, 88, 112, 119, 136, 154, 176, 187, 224, 238, 272, 308, 352, 374, 448, 476, 544, 616, 704, 748, 952, 1088, 1232, 1309, 1496, 1904, 2464, 2618, 2992, 3808, 4928, 5236, 5984, 7616, 10472, 11968, 20944, 41888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83762 and 83776. The biggest common factor number is the GCF number.
So the greatest common factor 83762 and 83776 is 14.

Also check out the Least Common Multiple of 83762 and 83776