On this page we will define the GCF of 61 and 21, teach you the different ways of calculating the GCF of 61 and 21, and show you what you can use the GCF of 61 and 21 for.
What is the GCF of 61 and 21?
GCF is the abbreviation for Greatest Common Factor. Therefore, the GCF of 61 and 21 is the same as the Greatest Common Factor of 61 and 21. The GCF of 61 and 21 is the largest positive integer by which both 61 and 21 can be divided. Furthermore, both 61 and 21 have a set of factors and the GCF is the greatest factor that 61 and 21 have in common.
Compare factors to get GCF of 61 and 21
Per definition above, to find the GCF of 61 and 21, you can compare the factors of 61 with the factors of 21 to see which factor is the greatest. When we did that, we found that the Greatest Common Factor (GCF) of 61 and 21 is 1.
Use LCM to get GCF of 61 and 21
The Least Common Multiple (LCM) of 61 and 21 is 1281. You can find the GCF of 61 and 21 by dividing the product of 61 and 21 by the LCM of 61 and 21. Here is the formula and math:
 = GCF 
 = 1 
Use computer spreadsheet to get GCF of 61 and 21
If you have a computer, you can also use a spreadsheet in Excel or Numbers to calculate the GCF of 61 and 21. You want to type =gcf(61, 21) into a cell to get the answer.
gcf(61, 21) = 1
Use the GCF of 61 and 21 to simplify a fraction
The GCF of 61 and 21 can be used for many things. You can, for example, simplify a fraction by dividing the numerator and denominator by the GCF like this:
 = 

Use GCF of 61 and 21 to simplify a ratio
Similarly, you can use the GCF of 61 and 21 to simplify a ratio by dividing each part of the ratio by the GCF like this:
= 61 : 21
= (61 ÷ 1) : (21 ÷ 1)
= 61 : 21
Use the GCF of 61 and 21 to find the LCM of 61 and 21
Since using the Least Common Multiple (LCM) is one of the ways to find the GCF of 61 and 21, you can use the GCF of 61 and 21 to find the LCM of 61 and 21. The LCM of 61 and 21 can, for example, be used to add and subtract fractions with denominators of 61 and 21. The LCM of 61 and 21 is the product of 61 and 21 divided by the GCF of 61 and 21. Here is the math:
 = LCM 
 = 1281 
That is all there is to it! We hope this page accomplished its goal of defining the GCF of 61 and 21 by showing you how to calculate the GCF, examples of its uses, and how it relates to LCM.
GCF Calculator
Use the GCF Calculator to solve a problem similar to the one explained on this page.
GCF of 61 and 22
Here is the next GCF on our list that we have calculated and explained for you.
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