# GCF of 75 and 100

Created by: Team Maths - Examples.com, Last Updated: May 30, 2024

## GCF of 75 and 100

The greatest common factor (GCF) of 75 and 100 is 25. To determine the GCF, you can identify the common factors of both numbers, which are 1, 5, and 25. Among these, 25 is the largest number that divides both 75 and 100 without leaving a remainder. Therefore, the GCF of 75 and 100 is 25, indicating that 25 is the greatest common divisors shared by both numbers.

## GCF of 75 and 100 by Prime Factorization Method.

To find the greatest common factor (GCF) of 75 and 100 using the prime factorization method:

Step 1: Prime factorize both numbers:

For 75: 75 = 3 × 5²

For 100: 100 = 2²×5²

Step 2: Identify common prime factors and their lowest powers:

• Both 75 and 100 have a common prime factor of 5², but 100 also has an additional factor of 2².

Step 3: Multiply the common prime factors with their lowest powers:

GCF = 5²= 25

Therefore, the greatest common factor (GCF) of 75 and 100 by prime factorization method is 25.

## GCF of 75 and 100 by Long Division Method.

To find the greatest common factor (GCF) of 75 and 100 using the long division method:

Step 1: Start by dividing the larger number (100) by the smaller number (75).

100 ÷ 75 = 1 with a remainder of 25.

Step 2: Then, take the divisor (75) and divide it by the remainder (25).

75 ÷ 25 =3.

Step 3: Continue this process until there is no remainder.

25 ÷ 3 = 8 with a remainder of 1.

3 ÷ 1 = 3.

1 ÷ 3 = 0.

Step 4: The last divisor before reaching 0 is the greatest common factor (GCF).

GCF = 25.

## GCF of 75 and 100 by Listing Common Factors.

To find the greatest common factor (GCF) of 75 and 100 by listing common factors:

Step 1: List the factors of each number.

Factors of 75: 1, 3, 5, 15, 25, 75

Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

Step 2: Identify the common factors. Common factors: 1, 5, 25

Step 3: Determine the greatest common factor. GCF=25.

Therefore, the greatest common factor (GCF) of 75 and 100 by listing common factors is 25.

## Can you find the GCF of 75 and 100 using a calculator?

Can you find the GCF of 75 and 100 using a calculator?

## Can you use the GCF of 75 and 100 to solve problems involving factors and multiples?

Yes, the techniques used to find the GCF of 75 and 100 are generally applicable to finding the GCF of any two numbers.

## How does the GCF of 75 and 100 relate to the concept of greatest common divisor?

The GCF of 75 and 100 is the greatest common divisor, as it represents the largest divisor common to both numbers.

## Can you find the GCF of 75 and 100 using a calculator?

Yes, most calculators have functions to calculate the GCF of two numbers.

## How many common factors do 75 and 100 have?

75 and 100 have three common factors: 1, 5, and 25.

## How do you calculate the GCF of 75 and 100?

You can calculate the GCF of 75 and 100 using methods such as prime factorization, listing common factors, or long division.

Text prompt