GCF of 12 and 15

Created by: Team Maths - Examples.com, Last Updated: May 29, 2024

GCF of 12 and 15

To find the Greatest Common Factor (GCF) of 12 and 15, you can use various methods such as listing common factors, prime factorization, and the long division method. By listing the factors, we see that the numbers factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 15 are 1, 3, 5, and 15. The common factors are 1 and 3, with the greatest common factor being 3. Using the prime factorization method, 12 is 2² × 3 and 15 is 3 × 5, with the common prime factor being 3. Using the long division method, dividing 15 by 12 gives a remainder of 3, and dividing 12 by 3 gives a remainder of 0, confirming that the GCF is 3. Thus, the GCF of 12 and 15 is 3.

Methods to Find GCF of 12 and 15

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

GCF of 12 and 15 by Prime Factorization Method.

To find the Greatest Common Factor (GCF) of 12 and 15 using the prime factorization method, follow these steps:

Step 1: Find the prime factorization of each number

Prime factorization of 12:

12 = 2 × 2 × 3 = 2² × 3

Prime factorization of 15:

15 = 3 × 5

Step 2: Identify the common prime factors

The only common prime factor of 12 and 15 is 3.

Step 3: Multiply the common prime factors

Since the only common prime factor is 3, the GCF is 3.

GCF of 12 and 15 by Long Division Method.

To find the Greatest Common Factor (GCF) of 12 and 15 using the long division method, follow these steps:

Step 1: Divide the larger number by the smaller number

15 ÷ 12 = 1 with a remainder of 3.

Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder

Now, we have 12 and 3.

Step 3: Repeat the division

12 ÷ 3 = 4 with a remainder of 0.

Step 4: When the remainder is 0, the divisors is the GCF

The last non-zero remainder is 3. So, the GCF of 12 and 15 is 3.

GCF of 12 and 15 by Listing Common Factors.

To find the Greatest Common Factor (GCF) of 12 and 15 by listing common factors, follow these steps:

Step 1: List the factors of each number

Factors of 12:

1, 2, 3, 4, 6, 12

Factors of 15:

1, 3, 5, 15

Step 2: Identify the common factors

Common factors of 12 and 15:

1, 3

Step 3: Determine the greatest common factor

The largest common factor is 3. Therefore, the GCF of 12 and 15 is 3.

How do you find the GCF of 12 and 15?

Use methods like long division, listing common factors, and prime factorization to find the GCF of 12 and 15.

What is the prime factorization of 15?

The prime factorization of 15 is 3 × 5.

What are the factors of 12?

The factors of 12 are 1, 2, 3, 4, 6, and 12.

How does the GCF help in simplifying fractions?

The GCF can be used to divide both the numerator and the denominator to simplify a fraction.

Can the GCF of 12 and 15 be one of the numbers?

Yes, if one number is a multiple of the other. For 12 and 15, the GCF is 3.

What is the prime factorization of 12?

The prime factorization of 12 is 2² × 3.

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