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

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1.GCF the 72 and 120
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Answer: GCF of 72 and 120 is 24.

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Explanation:

The GCF of 2 non-zero integers, x(72) and y(120), is the best positive essence m(24) that divides both x(72) and also y(120) without any remainder.


Let's look in ~ the various methods because that finding the GCF the 72 and also 120.

Long division MethodListing common FactorsUsing Euclid's Algorithm

GCF the 72 and also 120 by long Division

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GCF of 72 and also 120 is the divisor the we get when the remainder i do not care 0 after doing long department repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will divide the divisor of action 1 (72) through the remainder (48).Step 3: Repeat this process until the remainder = 0.

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

GCF the 72 and also 120 by Listing common Factors

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Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

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

GCF that 72 and 120 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode 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 mode 48) = GCF(48, 24)GCF(48, 24) = GCF(24, 48 mod 24) = GCF(24, 0)GCF(24, 0) = 24 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

Therefore, the value of GCF the 72 and 120 is 24.