# What is the GCF of 30 and 72?

GCF (Greatest Common Factor) of 30 and 72 is the largest possible number which divides both 30 and 72 exactly.

## Answer: GCF of 30 and 72 is 6

GCF of 30 and 72 is the highest number that divides 30 and 72 exactly leaving the remainder 0.

**Explanation:**

The greatest common factor of two numbers x and y is the greatest number that divides x and y leaving the remainder as 0

We can find the GCF of 30 and 72 by the following methods.

- GCF of 30 and 72 by Long Division Method
- GCF of 30 and 72 by Listing the Common Factors Method

### Method 1: GCF of 30 and 72 by Long Division

The steps to find the GCF(30, 72) are shown below:

**Step 1:** Divide 72 with 30 and check the remainder.

**Step 2:** Make the remainder 12 as the new divisor and the previous divisor 30 as the new dividend and perform the long division again.

**Step 3:** Continue this process till you obtain the remainder as 0 and the last divisor is our GCF of 30 and 72

Since the last divisor in the division process is 6, the GCF of 30 and 72 is 6

### Method 2: GCF of 30 and 72 by Listing the Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Clearly, the common factors of 30 and 72 are 1, 2, 3 and 6

The greatest common factor is 6

So, GCF of 30 and 72 is 6

Irrespective of the method, the solution to our question GCF of 30 and 72 is the same.