GCF of 72 and also 120 is the largest possible number the divides 72 and 120 specifically without any kind of remainder. The determinants of 72 and 120 space 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 space 3 generally used techniques to find the GCF of 72 and 120 - long division, Euclidean algorithm, and prime factorization.

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1. | GCF the 72 and 120 |

2. | List that Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF the 72 and also 120 is 24.

**Explanation: **

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

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

Long division MethodListing typical FactorsUsing Euclid's Algorithm### GCF that 72 and also 120 by long Division

GCF the 72 and also 120 is the divisor that we gain when the remainder i do not care 0 ~ 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 procedure until the remainder = 0.

The equivalent divisor (24) is the GCF that 72 and 120.

### GCF the 72 and 120 by Listing usual Factors

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

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

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

### GCF of 72 and also 120 through Euclidean Algorithm

As every 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 also 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|, wherein X ≠ 0)Therefore, the value of GCF that 72 and 120 is 24.