What is the Greatest Common Factor of 32025 and 32040?

Greatest common factor (GCF) of 32025 and 32040 is 15.

GCF(32025,32040) = 15

We will now calculate the prime factors of 32025 and 32040, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32025 and 32040.

How to find the GCF of 32025 and 32040?

We will first find the prime factorization of 32025 and 32040. After we will calculate the factors of 32025 and 32040 and find the biggest common factor number .

Step-1: Prime Factorization of 32025

Prime factors of 32025 are 3, 5, 7, 61. Prime factorization of 32025 in exponential form is:

32025 = 3¹ × 5² × 7¹ × 61¹

Step-2: Prime Factorization of 32040

Prime factors of 32040 are 2, 3, 5, 89. Prime factorization of 32040 in exponential form is:

32040 = 2³ × 3² × 5¹ × 89¹

Step-3: Factors of 32025

List of positive integer factors of 32025 that divides 32025 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 61, 75, 105, 175, 183, 305, 427, 525, 915, 1281, 1525, 2135, 4575, 6405, 10675

Step-4: Factors of 32040

List of positive integer factors of 32040 that divides 32025 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 89, 90, 120, 178, 180, 267, 356, 360, 445, 534, 712, 801, 890, 1068, 1335, 1602, 1780, 2136, 2670, 3204, 3560, 4005, 5340, 6408, 8010, 10680, 16020

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32025 and 32040. The biggest common factor number is the GCF number.
So the greatest common factor 32025 and 32040 is 15.

Also check out the Least Common Multiple of 32025 and 32040