Home » Greatest Common Factor » GCF of 49 and 7

GCF of 49 and 7

The gcf of 49 and 7 is the largest positive integer that divides the numbers 49 and 7 without a remainder. Spelled out, it is the greatest common factor of 49 and 7. Here you can find the result for 49 and 7, along with a total of three methods for computing it.


7

This Greatest Common Factor Calculator is Really Cool! Click To TweetYou should check out our calculator. Not only can it determine the outcome of 49 and 7, but also that of three or more integers including forty-nine and seven for example. Keep reading to learn everything about the gcf (49,7) and the terms related to it.

What is the Greatest Common Factor of 49 and 7?

If you just want to know what is the greatest common factor of 49 and 7, it is 7. Usually, this is written as

gcf(49,7) = 7


The gcf of 49 and 7 can be obtained like this:
  • The factors of 49 are 49, 7, 1.
  • The factors of 7 are 7, 1.
  • The common factors of 49 and 7 are 7, 1, intersecting the two sets above.
  • In the intersection factors of 49 ∩ factors of 7 the greatest element is 7.
  • Therefore, the greatest common factor of 49 and 7 is 7.

Taking the above into account you also know how to find all the common factors of 49 and 7, not just the greatest. In the next section we show you how to calculate the gcf of forty-nine and seven by means of two more methods.

How to find the GCF of 49 and 7

The greatest common factor of 49 and 7 can be computed by using the least common multiple aka lcm of 49 and 7. This is the easiest approach:

gcf (49,7) = = 7



Alternatively, the gcf of 49 and 7 can be found using the prime factorization of 49 and 7:
  • The prime factorization of 49 is: 7 x 7
  • The prime factorization of 7 is: 7
  • The prime factors and multiplicities 49 and 7 have in common are: 7
  • 7 is the gcf of 49 and 7
  • gcf(49,7) = 7

In any case, the easiest way to compute the result for two numbers like 49 and 7 is by using our calculator above. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 49,7. The calculation is conducted automatically.

Similar searched terms on our site also include:

In the next paragraph we explain how the mathematical concept can be employed.

Keep reading – it’s really interesting.

Use of Greatest Common Factor of 49 and 7

What is the greatest common factor of 49 and 7 used for? Answer: It is helpful for reducing fractions like 49 / 7. Just divide the nominator as well as the denominator by the gcf (49,7) to reduce the fraction to lowest terms.

.

Next, we shed a light on the mathematical properties.

Properties of GCF of 49 and 7

The most important properties of the gcf(49,7) are:

  • Commutative property: gcf(49,7) = gcf(7,49)
  • Associative property: gcf(49,7,n) = gcf(gcf(7,49),n)

The associativity is particularly useful to get the gcf of three or more numbers; our calculator makes use of it.

Summary

Note that you can find the greatest common factor of many integer pairs including forty-nine / seven by using the search form in the sidebar of this page.

Questions and comments are really appreciated. Use the form below or send us a mail to get in touch.

Please hit the sharing buttons if our article about the greatest common factor of 49 and 7 has been useful to you, and make sure to bookmark our site.

If you have some time left check out the related sites and resources in the sidebar of this site.

Thanks for your visit.

– Article written by Mark, last updated on August 8th, 2023