## GCF and LCM of 72 and 90

### Enter GCF or LCM numbers:

Determine the Greatest Common Factor (GCF) of (72,90)

### Determine the factors for 72 up to 72 since that is the minimum of the 2 numbers

1,2,3,4,6,8,9,12,18,24,36,72### Determine the factors for 90 up to 72 since that is the minimum of the 2 numbers

1,2,3,5,6,9,10,15,18,30,45The common factors between them are 1,2,3,6,9,18

The greatest common factor between them is **18**

Since the Greatest Common Factor of both numbers ≠ 1, the numbers are

__not__relatively prime (co-prime)

Since the Greatest Common Factor of Both Numbers is both ≠ 1 and have a difference of two, the numbers are not twin prime

To see the LCM of these numbers, click the LCM button above

Determine the Least Common Multiple (LCM) of (72,90)

We start by listing out each multiple for our 2 numbers

The LCM is the smallest multiple common in all the lists

### List the first few multiples for 72

72,,,,,,,### List the first few multiples for 90

90,,,,,,Our Least Common Multiple (LCM) of (72,90) is

### Greatest Common Factor and Least Common Multiple Video

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## GCF of 72 and 90

### FAQs on GCF of 72 and 90

### What is the GCF of 72 and 90?

The ** GCF of 72 and 90 is 18**. To calculate the GCF (Greatest Common Factor) of 72 and 90, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 72 and 90, i.e.,

### If the GCF of 90 and 72 is 18, Find its LCM.

GCF(90, 72) × LCM(90, 72) = 90 × 72

Since the GCF of 90 and 72 = 18

⇒ 18 × LCM(90, 72) =

Therefore, LCM =

☛ GCF Calculator

### What are the Methods to Find GCF of 72 and 90?

There are three commonly used methods to find the **GCF of 72 and 90**.

- By Long Division
- By Listing Common Factors
- By Prime Factorization

### How to Find the GCF of 72 and 90 by Long Division Method?

To find the GCF of 72, 90 using long division method, 90 is divided by The corresponding divisor (18) when remainder equals 0 is taken as GCF.

### How to Find the GCF of 72 and 90 by Prime Factorization?

To find the GCF of 72 and 90, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 90 = 2 × 3 × 3 × 5.

⇒ Since 2, 3, 3 are common terms in the prime factorization of 72 and Hence, GCF(72, 90) = 2 × 3 × 3 = 18

☛ Prime Numbers

### What is the Relation Between LCM and GCF of 72, 90?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 72 and 90, i.e. GCF × LCM = 72 ×

Sours: https://www.cuemath.com/numbers/gcf-ofand/

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## What is the Greatest Common Factor (GCF) of 72 and 90?

Are you on the hunt for the GCF of 72 and 90? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!

Want to quickly learn or show students how to find the GCF of two or more numbers? Play this very quick and fun video now!

First off, if you're in a rush, here's the answer to the question **"what is the GCF of 72 and 90?"**:

GCF of 72 and 90 = 18

### What is the Greatest Common Factor?

Put simply, the GCF of a set of whole numbers is the largest positive integer (i.e whole number and not a decimal) that divides evenly into all of the numbers in the set. It's also commonly known as:

- Greatest Common Denominator (GCD)
- Highest Common Factor (HCF)
- Greatest Common Divisor (GCD)

There are a number of different ways to calculate the GCF of a set of numbers depending how many numbers you have and how large they are.

For smaller numbers you can simply look at the factors or multiples for each number and find the greatest common multiple of them.

For 72 and 90 those factors look like this:

- Factors for 1, 2, 3, 4, 6, 8, 9, 12,
**18**, 24, 36, and 72 - Factors for 1, 2, 3, 5, 6, 9, 10, 15,
**18**, 30, 45, and 90

As you can see when you list out the factors of each number, 18 is the greatest number that 72 and 90 divides into.

### Prime Factors

As the numbers get larger, or you want to compare multiple numbers at the same time to find the GCF, you can see how listing out all of the factors would become too much. To fix this, you can use prime factors.

List out all of the prime factors for each number:

- Prime Factors for 2, 2, 2, 3, and 3
- Prime Factors for 2, 3, 3, and 5

Now that we have the list of prime factors, we need to find any which are common for each number.

Looking at the occurences of common prime factors in 72 and 90 we can see that the commonly occuring prime factors are 2, 3, and 3.

To calculate the prime factor, we multiply these numbers together:

GCF = 2 x 3 x 3 = 18

### Find the GCF Using Euclid's Algorithm

The final method for calculating the GCF of 72 and 90 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.

If you want to learn more about the algorithm and perhaps try it yourself, take a look at the Wikipedia page.

Hopefully you've learned a little math today and understand how to calculate the GCD of numbers. Grab a pencil and paper and give it a try for yourself. (or just use our GCD calculator - we won't tell anyone!)

### Cite, Link, or Reference This Page

If you found this content useful in your research, please do us a great favor and use the tool below to make sure you properly reference us wherever you use it. We really appreciate your support!

<a href="https://visualfractions.com/calculator/greatest-common-factor/gcf-ofand/">Greatest Common Factor of 72 and 90</a>

"Greatest Common Factor of 72 and 90".

*VisualFractions.com*. Accessed on October 28, https://visualfractions.com/calculator/greatest-common-factor/gcf-ofand/."Greatest Common Factor of 72 and 90".

*VisualFractions.com*, https://visualfractions.com/calculator/greatest-common-factor/gcf-ofand/. Accessed 28 October,Greatest Common Factor of 72 and VisualFractions.com. Retrieved from https://visualfractions.com/calculator/greatest-common-factor/gcf-ofand/.

On this page we will define the GCF of 72 and 90, teach you the different ways of calculating the GCF of 72 and 90, and show you what you can use the GCF of 72 and 90 for.

**What is the GCF of 72 and 90?**

GCF is the abbreviation for Greatest Common Factor. Therefore, the GCF of 72 and 90 is the same as the Greatest Common Factor of 72 and The GCF of 72 and 90 is the largest positive integer by which both 72 and 90 can be divided. Furthermore, both 72 and 90 have a set of factors and the GCF is the greatest factor that 72 and 90 have in common.

**Compare factors to get GCF of 72 and 90**

Per definition above, to find the GCF of 72 and 90, you can compare the factors of 72with the factors of 90to see which factor is the greatest. When we did that, we found that the Greatest Common Factor (GCF) of 72 and 90 is

**Use LCM to get GCF of 72 and 90**

The Least Common Multiple (LCM) of 72 and 90 is You can find the GCF of 72 and 90 by dividing the product of 72 and 90 by the LCM of 72 and Here is the formula and math:

= GCF |

= 18 |

**Use computer spreadsheet to get GCF of 72 and 90**

If you have a computer, you can also use a spreadsheet in Excel or Numbers to calculate the GCF of 72 and You want to type =gcf(72, 90) into a cell to get the answer.

**gcf(72, 90) = 18**

**Use the GCF of 72 and 90 to simplify a fraction**

The GCF of 72 and 90 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 72 and 90 to simplify a ratio**

Similarly, you can use the GCF of 72 and 90 to simplify a ratio by dividing each part of the ratio by the GCF like this:

= 72 : 90

= (72 ÷ 18) : (90 ÷ 18)

= 4 : 5

**Use the GCF of 72 and 90 to find the LCM of 72 and 90**

Since using the Least Common Multiple (LCM) is one of the ways to find the GCF of 72 and 90, you can use the GCF of 72 and 90 to find the LCM of 72 and The LCM of 72 and 90 can, for example, be used to add and subtract fractions with denominators of 72 and The LCM of 72 and 90 is the product of 72 and 90 divided by the GCF of 72 and Here is the math:

= LCM |

= |

That is all there is to it! We hope this page accomplished its goal of defining the GCF of 72 and 90 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 72 and 91**

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