# GCF of 15 and 25

Created by: Team Maths - Examples.com, Last Updated: May 24, 2024

## GCF of 15 and 25

To determine the greatest common factor (GCF) of 15 and 25, we can use various methods. One approach is by listing the factors of each number. For 15, the factors are 1, 3, 5, and 15. For 25, the factors are 1, 5, and 25. The common factor shared by both numbers is 5. Thus, the GCF of 15 and 25 is 5. Another method is through prime factorization. Breaking down 15 into prime factors yields 3×5, while 25 breaks down into 5×5. Identifying the common prime factors, we find 5. Hence, regardless of the method employed, the GCF of 15 and 25 remains 5, representing the largest number that divides both without a remainder.

## GCF of 15 and 25

### GCF of 15 and 25 is 5.

The greatest common factor (GCF) of 15 and 25 is 5. By listing factors or prime factorization, 5 emerges as the largest number dividing both without remainder, serving as their common divisor.

## Methods to Find GCF of 15 and 25

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

## GCF of 15 and 25 by Prime Factorization Method

To find the greatest common factor (GCF) of 15 and 25 using prime factorization, we break down each number into its prime factors.
For 15: 15 = 3 × 5
For 25 : 25 = 5 × 5
The common prime factor is 5. Therefore, the GCF of 15 and 25 is 5.

## GCF of 15 and 25 by Long Division Method.

Step 1: Divide the larger number (25) by the smaller number (15). 25 ÷ 15 = 1 with a remainder of 10

Step 2: Divide the divisor (15) by the remainder (10). 15 ÷ 10 = 1 with a remainder of 5

Step 3: Divide the divisor (10) by the remainder (5). 10 ÷ 5 = 2 with no remainder

Step 4: Since the remainder is now 0, stop. The divisor from the last division, which is 5, is the greatest common factor (GCF) of 15 and 25.

Therefore, the GCF of 15 and 25 by the long division method is 5.

## GCF of 15 and 25 by Listing Common Factors

To find the greatest common factor (GCF) of 15 and 25 by listing common factors, we identify numbers that divide evenly into both. For 15, the factors are 1, 3, 5, and 15. For 25, the factors are 1, 5, and 25. The largest common factor is 5. Therefore, the GCF of 15 and 25 is 5.

## How is the GCF of 15 and 25 calculated?

The GCF is found by identifying the largest number that divides both 15 and 25 without leaving a remainder, which in this case is 5.

## What are the common factors of 15 and 25?

The common factors of 15 and 25 are the numbers that divide both evenly, which are 1 and 5.

## Why is 5 the GCF of 15 and 25?

It’s because 5 is the largest number that divides both 15 and 25 without any remainder.

## How can the GCF of 15 and 25 be used in mathematics?

It can be used to simplify fractions, find common denominators, and solve various mathematical problems involving these two numbers.

## What real-life scenarios might involve finding the GCF of 15 and 25?

It can be useful in various situations like scaling measurements, determining common factors in sets of items, or dividing resources equally among groups.

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