What is the Greatest Common Factor of 19762 and 19776?

Greatest common factor (GCF) of 19762 and 19776 is 2.

GCF(19762,19776) = 2

We will now calculate the prime factors of 19762 and 19776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19762 and 19776.

How to find the GCF of 19762 and 19776?

We will first find the prime factorization of 19762 and 19776. After we will calculate the factors of 19762 and 19776 and find the biggest common factor number .

Step-1: Prime Factorization of 19762

Prime factors of 19762 are 2, 41, 241. Prime factorization of 19762 in exponential form is:

19762 = 2¹ × 41¹ × 241¹

Step-2: Prime Factorization of 19776

Prime factors of 19776 are 2, 3, 103. Prime factorization of 19776 in exponential form is:

19776 = 2⁶ × 3¹ × 103¹

Step-3: Factors of 19762

List of positive integer factors of 19762 that divides 19762 without a remainder.

1, 2, 41, 82, 241, 482, 9881

Step-4: Factors of 19776

List of positive integer factors of 19776 that divides 19762 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 103, 192, 206, 309, 412, 618, 824, 1236, 1648, 2472, 3296, 4944, 6592, 9888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19762 and 19776. The biggest common factor number is the GCF number.
So the greatest common factor 19762 and 19776 is 2.

Also check out the Least Common Multiple of 19762 and 19776