What is the Greatest Common Factor of 25760 and 25776?

Greatest common factor (GCF) of 25760 and 25776 is 16.

GCF(25760,25776) = 16

We will now calculate the prime factors of 25760 and 25776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25760 and 25776.

How to find the GCF of 25760 and 25776?

We will first find the prime factorization of 25760 and 25776. After we will calculate the factors of 25760 and 25776 and find the biggest common factor number .

Step-1: Prime Factorization of 25760

Prime factors of 25760 are 2, 5, 7, 23. Prime factorization of 25760 in exponential form is:

25760 = 2⁵ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 25776

Prime factors of 25776 are 2, 3, 179. Prime factorization of 25776 in exponential form is:

25776 = 2⁴ × 3² × 179¹

Step-3: Factors of 25760

List of positive integer factors of 25760 that divides 25760 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 23, 28, 32, 35, 40, 46, 56, 70, 80, 92, 112, 115, 140, 160, 161, 184, 224, 230, 280, 322, 368, 460, 560, 644, 736, 805, 920, 1120, 1288, 1610, 1840, 2576, 3220, 3680, 5152, 6440, 12880

Step-4: Factors of 25776

List of positive integer factors of 25776 that divides 25760 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 179, 358, 537, 716, 1074, 1432, 1611, 2148, 2864, 3222, 4296, 6444, 8592, 12888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25760 and 25776. The biggest common factor number is the GCF number.
So the greatest common factor 25760 and 25776 is 16.

Also check out the Least Common Multiple of 25760 and 25776