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. 68 is a composite number and has more than 2 factors, unlike the prime numbers. Hence, the factors of 68 are 1, 2, 4, 17, 34 and 68.

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.

What are Factors of 68?

Factors of 68 are the numbers that can divide the original number, evenly. There are a total of six factors of 68, they are 1, 2, 4, 17, 34 and 68. Each of these factors can divide 68 in equal number of parts.

Since, the number of factors are more than 2, therefore, 68 is a composite number. Here, the smallest factor of 68 is 1 and highest factor is 68 itself. Thus, we have simply evaluated the two factors of 68. After finding the factors we can arrange them in ascending order also. Let us learn to find the other factors in the next section.

How to Find Factors of 68?

Factors are the real numbers that divide the original number (in this case, 68), evenly or completely. As we learned, 1 is the factor of all the whole numbers. Also, a number is a factor of itself. Now, 68 is an even number therefore, it is divisible by 2. Hence, the quotient we get after division of 64 by 2, is also a factor of 68. Let us find all the factors now.

• 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 the 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.

Important Facts

• Factors of 68: 1, 2, 4, 17, 34, and 68
• Prime Factors of 68: 2 and 17
• Prime Factorisation of 68: 2² × 17
• Pair Factors of 68: (1,68), (2,34), and (4,17)
• Sum of Factors of 68: 126
• Highest factor of 68: 68
• Smallest factor of 68: 1

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Solved Examples on Factors of 68

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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