GCF of 60 and also 75 is the largest feasible number that divides 60 and also 75 precisely without any remainder. The determinants of 60 and 75 room 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and 1, 3, 5, 15, 25, 75 respectively. There are 3 frequently used techniques to uncover the GCF that 60 and also 75 - prime factorization, long division, and also Euclidean algorithm.

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 1 GCF that 60 and 75 2 List the Methods 3 Solved Examples 4 FAQs

Answer: GCF the 60 and also 75 is 15.

Explanation:

The GCF of two non-zero integers, x(60) and also y(75), is the biggest positive creature m(15) the divides both x(60) and y(75) without any remainder.

Let's look in ~ the various methods for finding the GCF that 60 and 75.

Using Euclid's AlgorithmLong department MethodListing common Factors

### GCF the 60 and also 75 through Euclidean Algorithm

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

Here X = 75 and Y = 60

GCF(75, 60) = GCF(60, 75 mod 60) = GCF(60, 15)GCF(60, 15) = GCF(15, 60 mod 15) = GCF(15, 0)GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF the 60 and 75 is 15.

### GCF of 60 and 75 by lengthy Division

GCF that 60 and also 75 is the divisor the we gain when the remainder i do not care 0 after ~ doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will divide the divisor of action 1 (60) through the remainder (15).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 60 and also 75.

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### GCF of 60 and also 75 by Listing common Factors

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60Factors of 75: 1, 3, 5, 15, 25, 75

There are 4 typical factors of 60 and also 75, that are 1, 3, 5, and also 15. Therefore, the greatest typical factor that 60 and 75 is 15.