Negative Gcf Calculator

The Negative GCF Calculator helps you find the Greatest Common Factor (GCF) of negative numbers. The GCF is the largest positive integer that divides two or more integers without leaving a remainder. When working with negative numbers, the GCF is always positive.

What is GCF?

The Greatest Common Factor (GCF), also known as the Greatest Common Divisor (GCD), is the largest positive integer that divides two or more integers without leaving a remainder. For example, the GCF of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 exactly.

GCF is commonly used in:

Simplifying fractions
Solving mathematical problems involving ratios
Working with proportions and measurements

Negative GCF

When calculating the GCF of negative numbers, the result is always positive. This is because the GCF represents the largest positive integer that divides all the given numbers, regardless of their signs. For example:

GCF of -12 and -18 is 6
GCF of -15 and 25 is 5
GCF of -20 and -30 is 10

Note: The sign of the numbers does not affect the GCF. The GCF is always positive.

How to Calculate GCF

To calculate the GCF of two or more numbers, follow these steps:

List all the positive divisors of each number.
Identify the common divisors shared by all numbers.
Select the largest common divisor.

For example, to find the GCF of 12 and 18:

Divisors of 12: 1, 2, 3, 4, 6, 12
Divisors of 18: 1, 2, 3, 6, 9, 18
Common divisors: 1, 2, 3, 6
GCF: 6

GCF(a, b) = largest positive integer that divides both a and b without leaving a remainder

Examples

Example 1: GCF of -12 and -18

Step 1: Ignore the negative signs (GCF is always positive).

Step 2: Find the GCF of 12 and 18.

Divisors of 12: 1, 2, 3, 4, 6, 12
Divisors of 18: 1, 2, 3, 6, 9, 18
Common divisors: 1, 2, 3, 6
GCF: 6

Result: The GCF of -12 and -18 is 6.

Example 2: GCF of -15 and 25

Step 1: Ignore the negative sign.

Step 2: Find the GCF of 15 and 25.

Divisors of 15: 1, 3, 5, 15
Divisors of 25: 1, 5, 25
Common divisors: 1, 5
GCF: 5

Result: The GCF of -15 and 25 is 5.

Example 3: GCF of -20 and -30

Step 1: Ignore the negative signs.

Step 2: Find the GCF of 20 and 30.

Divisors of 20: 1, 2, 4, 5, 10, 20
Divisors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common divisors: 1, 2, 5, 10
GCF: 10

Result: The GCF of -20 and -30 is 10.

FAQ

What is the difference between GCF and LCM?: The Greatest Common Factor (GCF) is the largest number that divides two or more numbers without leaving a remainder. The Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers.
Can the GCF of negative numbers be negative?: No, the GCF of negative numbers is always positive. The sign of the numbers does not affect the GCF.
How do I find the GCF of more than two numbers?: To find the GCF of more than two numbers, find the GCF of the first two numbers, then find the GCF of that result with the next number, and continue until you've processed all numbers.
Is the GCF the same as the GCD?: Yes, GCF and GCD (Greatest Common Divisor) are terms used interchangeably to refer to the same mathematical concept.
Can the GCF of two numbers be zero?: No, the GCF of two numbers cannot be zero. The GCF is defined as the largest positive integer that divides both numbers, and zero is not a positive integer.