GCF of 72 and 120 is the largest possible number that divides 72 and 120 exactly without any remainder. The factors of 72 and 120 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 72 and 120 - long division, Euclidean algorithm, and prime factorization.

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**Answer:** GCF of 72 and 120 is 24.

**Explanation: **

The GCF of two non-zero integers, x(72) and y(120), is the greatest positive integer m(24) that divides both x(72) and y(120) without any remainder.

Let's look at the different methods for finding the GCF of 72 and 120.

Long Division MethodListing Common FactorsUsing Euclid's Algorithm### GCF of 72 and 120 by Long Division

GCF of 72 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

**Step 2:**Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (48).

**Step 3:**Repeat this process until the remainder = 0.

The corresponding divisor (24) is the GCF of 72 and 120.

### GCF of 72 and 120 by Listing Common Factors

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

**Factors of 120:**1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 8 common factors of 72 and 120, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 72 and 120 is 24.

### GCF of 72 and 120 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and mod is the modulo operator.

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Here X = 120 and Y = 72

GCF(120, 72) = GCF(72, 120 mod 72) = GCF(72, 48)GCF(72, 48) = GCF(48, 72 mod 48) = GCF(48, 24)GCF(48, 24) = GCF(24, 48 mod 24) = GCF(24, 0)GCF(24, 0) = 24 (∵ GCF(X, 0) = |X|, where X ≠ 0)Therefore, the value of GCF of 72 and 120 is 24.