# GCF of 10 and 15

Created by: Team Maths - Examples.com, Last Updated: May 27, 2024

## GCF of 10 and 15

The Greatest Common Factors (GCF) of 10 and 15 is 5. This is determined by identifying the largest numbers that divides both 10 and 15 without leaving a remainder. The prime factorization of 10 is 2 × 5, and the prime factorization of 15 is 3 × 5. The common prime factor is 5, making it the GCF of 10 and 15.

## Methods to Find GCF of 10 and 15

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

## GCF of 10 and 15 by Prime Factorization Method

Prime Factorization of 10:

• 10 = 2 × 5

Prime Factorization of 15:

• 15 = 3 × 5

Identify Common Factors:

• The common prime factor between 10 and 15 is 5.

Determine the GCF:

Since the only common prime factor is 5, the GCF of 10 and 15 is 5.

## GCF of 10 and 15 by Long Division Method.

Divide the larger number (15) by the smaller number (10):

15 ÷ 10 gives a quotient of 1 and a remainder of 5.

Replace the larger number with the smaller number (10) and the smaller number with the remainder (5):

Now, divide 10 by 5.

10 ÷ 5 gives a quotient of 2 and a remainder of 0.

When the remainder is 0, the divisor at this step is the GCF:

The last divisors, which is 5, is the GCF.

Therefore, the GCF of 10 and 15 is 5.

## GCF of 10 and 15 by Listing Common Factors

List the factors of 10:

Factors of 10: 1, 2, 5, 10

List the factors of 15:

Factors of 15: 1, 3, 5, 15

Identify the common factors:

Common factors of 10 and 15: 1, 5

Determine the greatest common factor:

The greatest common factor is 5.

Therefore, the GCF of 10 and 15 is 5.

## Can the GCF of 10 and 15 be greater than 5?

No, the GCF of 10 and 15 cannot be greater than 5 because 5 is the largest number that divides both 10 and 15 without leaving a remainder.

## What are three common factors of 10 and 15?

Three common factors of 10 and 15 are 1 and 5. These are the only numbers that divide both 10 and 15 without leaving a remainder.

## What are the first 10 factors of 15?

The factors of 15 are 1, 3, 5, and 15. Since 15 is a relatively small number, it has only four factors. There are no additional factors.

## What are the first two common multiples of 10 and 15?

The first two common multiples of 10 and 15 are 30 and 60. These are the smallest numbers that are divisible by both 10 and 15 without leaving a remainder.

## How to find LCM of 10?

To find the Least Common Multiple (LCM) of 10 and another number, list the multiples of both numbers and identify the smallest common multiple. For example, multiples of 10 are 10, 20, 30, etc.

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