What is the Greatest Common Factor of 19810 and 19824?

Greatest common factor (GCF) of 19810 and 19824 is 14.

GCF(19810,19824) = 14

We will now calculate the prime factors of 19810 and 19824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19810 and 19824.

How to find the GCF of 19810 and 19824?

We will first find the prime factorization of 19810 and 19824. After we will calculate the factors of 19810 and 19824 and find the biggest common factor number .

Step-1: Prime Factorization of 19810

Prime factors of 19810 are 2, 5, 7, 283. Prime factorization of 19810 in exponential form is:

19810 = 2¹ × 5¹ × 7¹ × 283¹

Step-2: Prime Factorization of 19824

Prime factors of 19824 are 2, 3, 7, 59. Prime factorization of 19824 in exponential form is:

19824 = 2⁴ × 3¹ × 7¹ × 59¹

Step-3: Factors of 19810

List of positive integer factors of 19810 that divides 19810 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 283, 566, 1415, 1981, 2830, 3962, 9905

Step-4: Factors of 19824

List of positive integer factors of 19824 that divides 19810 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 59, 84, 112, 118, 168, 177, 236, 336, 354, 413, 472, 708, 826, 944, 1239, 1416, 1652, 2478, 2832, 3304, 4956, 6608, 9912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19810 and 19824. The biggest common factor number is the GCF number.
So the greatest common factor 19810 and 19824 is 14.

Also check out the Least Common Multiple of 19810 and 19824