What is the Greatest Common Factor of 83760 and 83776?

Greatest common factor (GCF) of 83760 and 83776 is 16.

GCF(83760,83776) = 16

We will now calculate the prime factors of 83760 and 83776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83760 and 83776.

How to find the GCF of 83760 and 83776?

We will first find the prime factorization of 83760 and 83776. After we will calculate the factors of 83760 and 83776 and find the biggest common factor number .

Step-1: Prime Factorization of 83760

Prime factors of 83760 are 2, 3, 5, 349. Prime factorization of 83760 in exponential form is:

83760 = 2⁴ × 3¹ × 5¹ × 349¹

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 83760

List of positive integer factors of 83760 that divides 83760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 349, 698, 1047, 1396, 1745, 2094, 2792, 3490, 4188, 5235, 5584, 6980, 8376, 10470, 13960, 16752, 20940, 27920, 41880

Step-4: Factors of 83776

List of positive integer factors of 83776 that divides 83760 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 83760 and 83776. The biggest common factor number is the GCF number.
So the greatest common factor 83760 and 83776 is 16.

Also check out the Least Common Multiple of 83760 and 83776