Is 13/78 a repeating decimal?

Here we will show you how to determine if 13/78 is a repeating decimal or a non-repeating decimal.

A repeating decimal is a decimal number that goes on forever. We want to know if the decimal number you get when you divide the fraction 13/78 (13 ÷ 78) is repeating or non-repeating.

Here are the steps to determine if 13/78 is a repeating decimal number:

1) Find the denominator of 13/78 in its lowest form.
The greatest common factor (GCF) of 13 and 78 is 13. Convert 13/78 to its simplest form by dividing the numerator and denominator by its GCF:

		13 ÷ 13
		78 ÷ 13

		1
		6

Thus, the denominator of 13/78 in its lowest form is 6.

2) Find the prime factors of the answer in Step 1.
The prime factors of 6 are all the prime numbers that you multiply together to get 6. The prime factors of 6 are:

2 x 3

3) Determine if 13/78 is repeating
A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all. This is the case here, which means that our answer is as follows:

13/78
= repeating

Repeating Decimal Calculator
Enter another fraction to determine if it is a repeating decimal.

Is 13/79 a repeating decimal?
Is the next fraction on our list a repeating decimal? Go here to find out!