# GCF of 8 and 10

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

## GCF of 8 and 10

The Greatest Common Factors (GCF) of 8 and 10 is 2. This is determined by identifying the largest numbers that divides both 8 and 10 without leaving a remainder. The prime factorization of 8 is 2³ (2 × 2 × 2) and the prime factorization of 10 is 2 × 5. The only common prime factor is 2, making it the GCF of 8 and 10.

## Methods to Find GCF of 8 and 10

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

## GCF of 8 and 10 by Prime Factorization Method

Prime Factorization of 8:

• 8 = 2 × 2 × 2 (or 2³)

Prime Factorization of 10:

• 10 = 2 × 5

Identify Common Factors:

• The common prime factor between 8 and 10 is 2.

Determine the GCF:

• Since the only common prime factor is 2, the GCF of 8 and 10 is 2.

## GCF of 8 and 10 by Long Division Method.

Divide the larger number (10) by the smaller number (8):

10 ÷ 8 gives a quotient of 1 and a remainder of 2.

Replace the larger number with the smaller number (8) and the smaller number with the remainder (2):

Now, divide 8 by 2.

8 ÷ 2 gives a quotient of 4 and a remainder of 0.

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

The last divisor, which is 2, is the GCF.

Therefore, the GCF of 8 and 10 is 2.

## GCF of 8 and 10 by Listing Common Factors

List the factors of 8:

Factors of 8: 1, 2, 4, 8

List the factors of 10:

Factors of 10: 1, 2, 5, 10

Identify the common factors:

Common factors of 8 and 10: 1, 2

Determine the greatest common factor:

The greatest common factor is 2.

Therefore, the GCF of 8 and 10 is 2.

## Why is the GCF of 8 and 10 important?

The GCF is important for simplifying fractions, solving problems involving ratios, and finding common denominators.

## Can the GCF of 8 and 10 be greater than 2?

No, the GCF of 8 and 10 cannot be greater than 2 because 2 is the largest number that divides both 8 and 10 without leaving a remainder.

## How is the GCF of 8 and 10 used in real-life situations?

The GCF is used in real-life situations such as dividing items into smaller sections, comparing quantities, and simplifying mathematical problems involving fractions.

## Can the GCF of 8 and 10 be found using a calculator?

Yes, many calculators have a function to find the GCF of two numbers. Simply input the numbers 8 and 10 and use the GCF or GCD function.

## What is 8 and 10 lowest common factor?

The lowest common factor of 8 and 10 is 1, as it is the smallest positive integer that divides both numbers without leaving a remainder.

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