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

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1. | GCF of 20 and 36 |

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**Answer:** GCF of 20 and 36 is 4.

**Explanation: **

The GCF of two non-zero integers, x(20) and y(36), is the greatest positive integer m(4) that divides both x(20) and y(36) without any remainder.

Let's look at the different methods for finding the GCF of 20 and 36.

Long Division MethodListing Common FactorsUsing Euclid's Algorithm### GCF of 20 and 36 by Long Division

GCF of 20 and 36 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 (20) by the remainder (16).

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

The corresponding divisor (4) is the GCF of 20 and 36.

### GCF of 20 and 36 by Listing Common Factors

**Factors of 20:**1, 2, 4, 5, 10, 20

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

There are 3 common factors of 20 and 36, that are 1, 2, and 4. Therefore, the greatest common factor of 20 and 36 is 4.

### GCF of 20 and 36 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 = 36 and Y = 20

GCF(36, 20) = GCF(20, 36 mod 20) = GCF(20, 16)GCF(20, 16) = GCF(16, 20 mod 16) = GCF(16, 4)GCF(16, 4) = GCF(4, 16 mod 4) = GCF(4, 0)GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)Therefore, the value of GCF of 20 and 36 is 4.