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| ▭\:\longdivision{▭} | \times \twostack{▭}{▭} | + \twostack{▭}{▭} | - \twostack{▭}{▭} | \left( | \right) | \times | \square\frac{\square}{\square} |
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| - \twostack{▭}{▭} | \lt | 7 | 8 | 9 | \div | AC |
| + \twostack{▭}{▭} | \gt | 4 | 5 | 6 | \times | \square\frac{\square}{\square} |
| \times \twostack{▭}{▭} | \left( | 1 | 2 | 3 | - | x |
| ▭\:\longdivision{▭} | \right) | . | 0 | = | + | y |
The Greatest Common Factor(GCF) is an important part of number theory. Whether you are a student learning factors, a teacher teaching the concept, or a professional dealing with number theory, understanding and working with the greatest common factor is essential. The Greatest Common Factor(GCF) Calculator is here to simplify the calculations for you, saving time and reducing errors.
In problems with large numbers or more than two numbers, finding the Greatest Common Factor(GCF), also known as the Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) can be challenging. The Greatest Common Factor(GCF) Calculator solves these problems by providing fast and accurate solutions. This guide will explain its features, benefits, and practical uses to make your math-solving experience easier.
The Greatest Common Factor(GCF) is the largest factor or divisor of the given two or more numbers. A factor is a positive integer that divides a number exactly leaving zero remainder. The Greatest Common Factor(GCF) is the highest possible number that can divide each of the two or more numbers completely without leaving any remainder. The Greatest Common Factor is also called the Greatest Common Divisor(GCD) or Highest Common Factor(HCF).
Identifying the Greatest Common Factor(GCF)
First, list all possible factors of each number
Now identify which is the largest factor or divisor common between each of the numbers.
Prime Factorisation Method of Finding the Greatest Common Factor(GCF)
First, break down each number to list all possible prime factors.
Now identify which all factors are common or shared between each of the numbers.
Now list and multiply the common factors.
The number achieved by multiplying the common factors is the highest or the Greatest Common Factor(GCF)
For example:
What is the Greatest Common Factor(GCF) of 6, 12 and 24
Step 1: Write the prime factorization of each number
6 = 2 x 3
12 = 2 x 2 x 3
24 = 2 x 2 x 2 x 3
Step 2: Identify the common factors shared among all the numbers
6 = 2 x 3
12 = 2 x 2 x 3
24 = 2 x 2 x 2 x 3
The only common factors of 6, 12 and 24 are 2 and 3.
Step 3: Multiply the common factors to find the Greatest Common Factor(GCF)
2 x 3 = 6
6 is the largest factor that can divide 6, 12 and 24 without leaving any remainder. Hence, 6 is the GCF or the greatest common factor of 6, 12 and 24
Factors are widely used in daily life, from cooking to finding the best possible fit in the fields of packaging, construction and engineering, finance and data analysis, etc.
Simplification and understanding of non-unit fractions, profit, and interest rates also become easier if one knows how to find the Greatest Common Factor (GCF).
Greatest Common Factor(GCF) among two numbers
Example: What is the Greatest Common Factor(GCF) of 10 and 15?
Solution: 5
Greatest Common Factor(GCF) among three or more numbers
Example: What is the Greatest Common Factor(GCF) of 6, 9 and 15
Solution: 3
Word Problems
Example: A company produces cookies in batches of 8 and 12. What is the largest box size that can be used to package both batches?
Solution: 4
The Symblob’s Greatest Common Factor(GCF) Calculator is a tool to solve various problems related to finding the highest common factor. Here are its main features:
Finding Greatest Common Factor(GCF)
The calculator finds the Greatest Common Factor(GCF) to two or more numbers. For example, it quickly finds that the Greatest Common Factor(GCF) of 128 and 136 is 8.
Performing Basic Operations
The calculator explains the solution using three methods:
Solve using Divisors
Solve using Prime Factors
Solve using the Euclidean Algorithm
Step-by-Step Explanations
The Greatest Common Factor (GCF) calculator offers detailed, step-by-step solutions to help users understand the math behind the result.
Method 1:
Solve using Divisors
Example Problem: What is the Greatest Common Factor(GCF) of 150 and 75
Solution Steps:
Step 1: The factors of 150
= 1, 2, 3, 5, 10, 50, 75, 150
Step 2: The factors of 75
= 1,3, 5, 15, 25, 75
Step 3: the biggest common factor is:
= 75
Method 2:
Solve using Prime Factors
Example Problem: What is the Greatest Common Factor(GCF) of 54 and 81
Solution Steps:
Step 1: Write the prime factorization of each number
54 = 2 x 3 x 3 x 3
81 = 3 x 3 x 3 x 3
Step 2: Prime factors common to 54 and 81 are
= 3 x 3 x 3
Step 3: Multiply the numbers
3 x 3 x 3 = 27
Method 3:
Solve using the Euclidean Algorithm
Example Problem: What is the Greatest Common Factor(GCF) of 30 and 18
Solution Steps:
The Euclidean algorithm is using the following property repeatedly: GCF (a,b) =GCF (b, a mod b)
Step 1: Arrange the numbers in ascending order i.e 18 and 30.
Step2: Take the smallest number as divisor
Step 3: Use the modulo operation using the number(s) and smallest number as divisor
30 mod 18 = 12
18 mod 12 = 6
6 mod 6 = 0
Step 4: gcf (30, 18)= gcf(18,12)
gcf (18, 12)= gcf ( 6,0)
Step 5: gcf( 30,18)= 6
Using the Greatest Common Factor(GCF) Calculator is simple. Follow these steps:
Input the Numbers
Enter the two numbers of which the Greatest Common Factor(GCF) needs to be calculated for. Separate the two numbers using commas while entering
The above steps can be followed for three or more numbers as well.
View the Result
Click the "GO" button on the right side of the screen.
See the result and step-by-step explanation.
The calculator can explain the solution using the below three method
Solution using divisors
Solution using prime factors
Solution using Euclidian athgorithm
Example:
Finding the Greatest Common Factor(GCF) of two number
Input: gcf 18,24
Output: 6
Finding the Greatest Common Factor(GCF) of three or more numbers
Input:gcf 35, 21, 56
Output: 7
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