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The gcf of 100 and 97 is the largest positive integer that divides the numbers 100 and 97 without a remainder. Spelled out, it is the greatest common factor of 100 and 97. Here you can find the result for 100 and 97, along with a total of three methods for computing it.
What is the Greatest Common Factor of 100 and 97?
If you just want to know what is the greatest common factor of 100 and 97, it is 1. Usually, this is written as
The gcf of 100 and 97 can be obtained like this:
- The factors of 100 are 100, 50, 25, 20, 10, 5, 4, 2, 1.
- The factors of 97 are 97, 1.
- The common factors of 100 and 97 are 1, intersecting the two sets above.
- In the intersection factors of 100 ∩ factors of 97 the greatest element is 1.
- Therefore, the greatest common factor of 100 and 97 is 1.
Taking the above into account you also know how to find all the common factors of 100 and 97, not just the greatest. In the next section we show you how to calculate the gcf of hundred and ninety-seven by means of two more methods.
How to find the GCF of 100 and 97
The greatest common factor of 100 and 97 can be computed by using the least common multiple aka lcm of 100 and 97. This is the easiest approach:
Alternatively, the gcf of 100 and 97 can be found using the prime factorization of 100 and 97:
- The prime factorization of 100 is: 2 x 2 x 5 x 5
- The prime factorization of 97 is: 97
- The prime factors and multiplicities 100 and 97 have in common are: 1
- 1 is the gcf of 100 and 97
- gcf(100,97) = 1
In any case, the easiest way to compute the result for two numbers like 100 and 97 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 100,97. The calculation is conducted automatically.
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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 100 and 97
What is the greatest common factor of 100 and 97 used for? Answer: It is helpful for reducing fractions like 100 / 97. Just divide the nominator as well as the denominator by the gcf (100,97) to reduce the fraction to lowest terms.
Next, we shed a light on the mathematical properties.
Properties of GCF of 100 and 97
The most important properties of the gcf(100,97) are:
- Commutative property: gcf(100,97) = gcf(97,100)
- Associative property: gcf(100,97,n) = gcf(gcf(97,100),n)
The associativity is particularly useful to get the gcf of three or more numbers; our calculator makes use of it.
Note that you can find the greatest common factor of many integer pairs including hundred / ninety-seven by using the search form in the sidebar of this page.
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