GCF of 42 and 77


The gcf of 42 and 77 is the largest positive integer that divides the numbers 42 and 77 without a remainder. Spelled out, it is the greatest common factor of 42 and 77. Here you can find the gcf of 42 and 77, along with a total of three methods for computing it. In addition, we have a calculator you should check out. Not only can it determine the gcf of 42 and 77, but also that of three or more integers including forty-two and seventy-seven for example. Keep reading to learn everything about the gcf (42,77) and the terms related to it.

What is the GCF of 42 and 77

If you just want to know what is the greatest common factor of 42 and 77, it is 7. Usually, this is written as

gcf(42,77) = 7

The gcf of 42 and 77 can be obtained like this:

  • The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1.
  • The factors of 77 are 77, 11, 7, 1.
  • The common factors of 42 and 77 are 7, 1, intersecting the two sets above.
  • In the intersection factors of 42 ∩ factors of 77 the greatest element is 7.
  • Therefore, the greatest common factor of 42 and 77 is 7.

Taking the above into account you also know how to find all the common factors of 42 and 77, not just the greatest. In the next section we show you how to calculate the gcf of forty-two and seventy-seven by means of two more methods.

How to find the GCF of 42 and 77

The greatest common factor of 42 and 77 can be computed by using the least common multiple aka lcm of 42 and 77. This is the easiest approach:

gcf (42,77) = $\frac{42 \times 77}{lcm(42,77)} = \frac{3234}{462}$ = 7

Alternatively, the gcf of 42 and 77 can be found using the prime factorization of 42 and 77:

  • The prime factorization of 42 is: 2 x 3 x 7
  • The prime factorization of 77 is: 7 x 11
  • The prime factors and multiplicities 42 and 77 have in common are: 7
  • 7 is the gcf of 42 and 77
  • gcf(42,77) = 7

In any case, the easiest way to compute the gcf of two numbers like 42 and 77 is by using our calculator below. Note that it can also compute the gcf of more than two numbers, separated by a comma. For example, enter 42,77. The calculation is conducted automatically.

The gcf is...
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Use of GCF of 42 and 77

What is the greatest common factor of 42 and 77 used for? Answer: It is helpful for reducing fractions like 42 / 77. Just divide the nominator as well as the denominator by the gcf (42,77) to reduce the fraction to lowest terms.

$\frac{42}{77} = \frac{\frac{42}{7}}{\frac{77}{7}} = \frac{6}{11}$.

Properties of GCF of 42 and 77

The most important properties of the gcf(42,77) are:

  • Commutative property: gcf(42,77) = gcf(77,42)
  • Associative property: gcf(42,77,n) = gcf(gcf(77,42),n) $\hspace{10px}n\hspace{3px}\epsilon\hspace{3px}\mathbb{Z}$

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

To sum up, the gcf of 42 and 77 is 7. In common notation: gcf (42,77) = 7.

If you have been searching for gcf 42 and 77 or gcf 42 77 then you have come to the correct page, too. The same is the true if you typed gcf for 42 and 77 in your favorite search engine.

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

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