Factors Of 68

Factors of 68 are the numbers, which divide the number 68 to give a quotient as a whole number. The factors of a number divide the original number uniformly. When we multiply the factors in pairs, we get the results as the original number. After finding the factors we can arrange them in ascending order also. 68 is a composite number and has more than 2 factors, unlike the prime numbers. Some of the more examples of composite numbers are, 24, 63, 81, 70, 216, 215, etc.

Multiples are different from the factors, as they give extended times of 68, such as 68, 136, 204, 272, 340, 408, 476, 544, 612, 680 and so on. Learn to find the factors of number 68, along with its prime factorisation, by reading the article completely.

Factors of 68

Also, read:

How to Find Factors of 68?

Factors are the real numbers that divide the original number (in this case, 68), evenly or completely.

  • 68 ÷ 1 = 68     
  • 68 ÷ 2 = 34
  • 68 ÷ 4 = 17
  • 68 ÷ 17 = 4
  • 68 ÷ 34 = 2  
  • 68 ÷ 68 = 1

Thus, the factors of 68 are 1, 2, 4, 17, 34, and 68

Factor Of 68 in Pairs

We can find the pair factors, by multiplying two numbers in a pair to get the original number as 68, such as;

  • 1 × 68 = 68
  • 2 × 34 = 68
  • 4 × 17 = 68

From the above process, we get, the pair factors of the number 68 are (1, 68), (2, 34) and (4, 17).  

In the same way, we can write the negative pair factors of 68, since multiplication of two negative numbers will result in the positive number.

  • -1 × -68 = 68
  • -2 × -34 = 68
  • -4 × -17 = 68

Therefore, negative pair factors are (-1, -68), (-2, -34) and (-4, -17).

Factors of 68 in Ascending Order

Since we have already obtained all the factors here for the number 68, let us arrange them in ascending order, such as:

1<2<4<17<34<68.

You can see from the above arrangement, the smallest factor is 1 and the largest factor is 68.

Prime Factorisation of 68

The number 68 is a composite number. Now let us find its prime factors.

  • The first step is to divide the number 68 with the smallest prime factor, i.e. 2 and divide the output again by 2 till you get a fraction or odd number.

68 ÷ 2 = 34

  • Now, again divide 34 by 2.

34 ÷ 2 = 17

  • Now, we know 17 is a prime number and it has only two factors; 1 and 17. Therefore, we cannot continue with the division method further.

Therefore, the prime factors of 64 are 2 and 17.

Prime Factorisation of 64 = 2 × 2 × 17 or 22 × 17

Solved Examples

Q.1: There are 68 students in the class. If there are 17 benches in the class, then how many students can sit on each bench?

Solution: Given, 

Number of students = 68

Number of benches in class room = 17

Number of students on each bench = 68/17 = 4

Therefore, on each bench, 4 students can be seated.

Q.2: Find the sum of all the factors of 68. 

Solution: The factors of 68 are 1, 7 and 68.

Sum = 1 + 2 + 4 + 17 + 34 + 68 = 126

Therefore, 126 is the required sum.

Q.3: What is the greatest common factor of 60 and 68?

Answer: Let us write the factors of both the numbers.

60 → 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

68 → 1, 2, 4, 17, 34, 68

Hence, the greatest common factor is only 4.

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Frequently Asked Questions – FAQs

What are the factors of 68?

There are a total of six factors of 68. These factors are 1, 2, 4, 17, 34 and 68.

How is 68 represented as the product of prime factors?

The prime factorisation of 68 is:
68 = 2 x 2 x 17

Is 3 a factor of 68?

No, 3 is not a factor of 68. 3 cannot divide 68 completely.

Is 68 a prime number?

No, 68 is a composite number because it has more than 2 factors.

Is 68 a perfect square?

No, 68 is not a perfect square because the root of 68 is not a whole number but an irrational number.
√68 = 8.2462112512353

Test your knowledge on Factors of 68

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