GCF of 2 and 3

Find the Greatest Common Factor (GCF) of 2 and 3 with a complete step-by-step solution. The GCF is the largest number that divides both numbers without leaving a remainder.

Answer: GCF(2, 3) = 1

Step-by-Step Solution

Step 1 Find the Factors of 2

To find the GCF of 2 and 3, we first need to find all factors of each number.

The factors of 2 are numbers that divide 2 evenly:

1 × 2 = 2

Factors of 2: 1, 2

Step 2 Find the Factors of 3

Now we find all factors of 3:

1 × 3 = 3

Factors of 3: 1, 3

Step 3 Find the Common Factors

The common factors are numbers that appear in both lists:

Factors of 2: 1, 2

Factors of 3: 1, 3

Common factors: 1

The Greatest Common Factor is the largest of these: 1

Step 4 Prime Factorization Method

We can also find the GCF using prime factorization:

2 = 2

3 = 3

Take the common prime factors with the lowest powers:

GCF = 1 = 1

Step 5 Euclidean Algorithm

The Euclidean algorithm is a fast way to find the GCF using repeated division:

3 = 1 × 2 + 1

2 = 2 × 1 + 0

When the remainder is 0, the GCF is the last divisor: 1

Step 6 Final Answer

GCF(2, 3) = 1

GCF of 2 and 3

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