GCF of 3 and 4

Find the Greatest Common Factor (GCF) of 3 and 4 with a complete step-by-step solution. The GCF is the largest number that divides both numbers without leaving a remainder.

Answer: GCF(3, 4) = 1

Step-by-Step Solution

Step 1 Find the Factors of 3

To find the GCF of 3 and 4, we first need to find all factors of each number.

The factors of 3 are numbers that divide 3 evenly:

1 × 3 = 3

Factors of 3: 1, 3

Step 2 Find the Factors of 4

Now we find all factors of 4:

1 × 4 = 4, 2 × 2 = 4

Factors of 4: 1, 2, 4

Step 3 Find the Common Factors

The common factors are numbers that appear in both lists:

Factors of 3: 1, 3

Factors of 4: 1, 2, 4

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:

3 = 3

4 = 2^2

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:

4 = 1 × 3 + 1

3 = 3 × 1 + 0

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

Step 6 Final Answer

GCF(3, 4) = 1

GCF of 3 and 4

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