What is the Greatest Common Factor of 81760 and 81774?

Greatest common factor (GCF) of 81760 and 81774 is 14.

GCF(81760,81774) = 14

We will now calculate the prime factors of 81760 and 81774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81760 and 81774.

How to find the GCF of 81760 and 81774?

We will first find the prime factorization of 81760 and 81774. After we will calculate the factors of 81760 and 81774 and find the biggest common factor number .

Step-1: Prime Factorization of 81760

Prime factors of 81760 are 2, 5, 7, 73. Prime factorization of 81760 in exponential form is:

81760 = 2⁵ × 5¹ × 7¹ × 73¹

Step-2: Prime Factorization of 81774

Prime factors of 81774 are 2, 3, 7, 11, 59. Prime factorization of 81774 in exponential form is:

81774 = 2¹ × 3² × 7¹ × 11¹ × 59¹

Step-3: Factors of 81760

List of positive integer factors of 81760 that divides 81760 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 73, 80, 112, 140, 146, 160, 224, 280, 292, 365, 511, 560, 584, 730, 1022, 1120, 1168, 1460, 2044, 2336, 2555, 2920, 4088, 5110, 5840, 8176, 10220, 11680, 16352, 20440, 40880

Step-4: Factors of 81774

List of positive integer factors of 81774 that divides 81760 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 59, 63, 66, 77, 99, 118, 126, 154, 177, 198, 231, 354, 413, 462, 531, 649, 693, 826, 1062, 1239, 1298, 1386, 1947, 2478, 3717, 3894, 4543, 5841, 7434, 9086, 11682, 13629, 27258, 40887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81760 and 81774. The biggest common factor number is the GCF number.
So the greatest common factor 81760 and 81774 is 14.

Also check out the Least Common Multiple of 81760 and 81774