What is the Greatest Common Factor of 81970 and 81984?

Greatest common factor (GCF) of 81970 and 81984 is 14.

GCF(81970,81984) = 14

We will now calculate the prime factors of 81970 and 81984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81970 and 81984.

How to find the GCF of 81970 and 81984?

We will first find the prime factorization of 81970 and 81984. After we will calculate the factors of 81970 and 81984 and find the biggest common factor number .

Step-1: Prime Factorization of 81970

Prime factors of 81970 are 2, 5, 7, 1171. Prime factorization of 81970 in exponential form is:

81970 = 2¹ × 5¹ × 7¹ × 1171¹

Step-2: Prime Factorization of 81984

Prime factors of 81984 are 2, 3, 7, 61. Prime factorization of 81984 in exponential form is:

81984 = 2⁶ × 3¹ × 7¹ × 61¹

Step-3: Factors of 81970

List of positive integer factors of 81970 that divides 81970 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 1171, 2342, 5855, 8197, 11710, 16394, 40985

Step-4: Factors of 81984

List of positive integer factors of 81984 that divides 81970 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 61, 64, 84, 96, 112, 122, 168, 183, 192, 224, 244, 336, 366, 427, 448, 488, 672, 732, 854, 976, 1281, 1344, 1464, 1708, 1952, 2562, 2928, 3416, 3904, 5124, 5856, 6832, 10248, 11712, 13664, 20496, 27328, 40992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81970 and 81984. The biggest common factor number is the GCF number.
So the greatest common factor 81970 and 81984 is 14.

Also check out the Least Common Multiple of 81970 and 81984