What are the Factors of 68 | Prime Factorization and Factor Tree of 68

Factors of 68 are the numerals that will divide the number 68 to give the remainder as a whole number. These factors of the number can be divided by the original number without leaving any remainder. And when it comes to multiplying those factors in pairs, we will get the original number as a result. 68 is also a composite number with factors that are both negative and positive. Let us learn how to find factors of 68 along with solved examples.

What Are the Factors of 68?

Factors are the numbers that divide the original number without leaving any remainder. In the case of 68, the numbers 1, 2, 4, 17, 34, and 68 are the numbers that divide the number 68 without leaving any remainder. Therefore, the number 68 has six factors, and they are 1, 2, 4, 17, 34, and 68.

Since 68 is a composite number, it has more than 2 factors, which are both positive and negative. Hence, the positive and negative factors of 68 are given below:

Positive 68 Factors	Negative 68 Factors
1	-1
2	-2
4	-4
17	-17
34	-34
68	-68

Write Factors of 68 in Pairs?

Here are the pairs factors of 68:

Positive Pair Factors of 68

the positive 68 pair factors are (1, 68), (2, 34), and (4, 17).

Negative Pair Factors of 68

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

How To Find Factors of 68 by Division method?

You can find 68 factors through the division method. For that, you will have to divide the number 68 by the sequence of natural numbers up to 68. A number that is divided by 68 and doesn’t leave any remainder are considered as 68 factors. The details on how to find factors of number 68 are given below:

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

As we can see, none of these numbers leaves a remainder after division, so that means 1, 2, 4, 17, 34, and 68 are the 68 factors.

What Is the Prime Factorisation of 68?

To find prime factors of 68, we will be using prime factorization method. The steps to find prime factors of 68 are given below:

• Step 1: Divide the number 68 with the least prime number. Hence, the least prime number that is divisible by 68 is 2.
• Step 2: When 68 is divided by 2, we will get the number 34.
• Step 3: Since 34 is a composite number, we have to split it again.
• Step 4: We’ll divide 34 into 2 and 17.
• Step 5: Since 2 and 17 are prime numbers, we cannot split them.

Hence the prime factors of 68 are 2 X 2 X 17 = 68.

Below is a picture for you to understand it more briefly:

Write the Factor Tree of 68.

We can also find the prime factors of the number 68 using the factor tree method. The steps to find prime factors of number 68 using the factor tree method are given below:

• Step 1: Place the number 68 at the top of the factor tree.
• Step 2: Now, as the tree branches, we will write down the pair factors of 2. Here we are using the pair factor 2 and 34 as the first branch of 68.
• Step 3: Since 2 is a prime number, we can no longer separate it.
• Step 4: But we can split 34 into 2 and 17. Since 2 and 17 are prime numbers, we can not split them anymore.

Hence, circling all the branches gives us factors 2, 2, and 17. Therefore, the prime factors of 68 using a factor tree are 2 X 2 X 17 = 68.

The factor tree of 68 is given below:

Solved Examples on Factors of 68

Here are some solved examples of 68 factors.

What is the sum of all the Factors of 68?
Factors of number 68 are 1, 2, 4, 17, 34, and 68.
Hence adding 1 + 2 + 4 + 17 + 34 + 68 = 126
The sum of factors of 68 is 126.

What are the factors and prime factors of 68?
The factors of 68 are 1, 2, 4, 17, 34, and 68.
The 68 prime factors are 2, 2, and 17.

What is the highest common factor between 78 and 68?
78 factors: 1, 2, 3, 6, 13, 26, 39, and 78.
68 factors: 1, 2, 4, 17, 34, and 68.
Hence the common factors of 4 and 6 are 1, and 2.
Therefore the highest common factor between 78 and 68 is 2.

What’s the highest common factor of 24 and 68?
Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24.
68 Factors: 1, 2, 4, 17, 34, and 68.
From the above, the common factors of 24 and 68 are 1, 2, and 4.
Hence the highest common factor of 24 and 68 is 4.

What’s the highest common factor of 56 and 68?
Factors of 56: 1, 2, 4, 7, 8, 14, 28, and 56.
Factors of 68: 1, 2, 4, 17, 34, and 68.
From the above, the common factors of 56 and 68 are 1, 2, and 4.
Hence the highest common factor of 56 and 68 is 4.

FAQs on Factors of 68

The frequently asked questions on 68 factors are given below:

List all the factors of 68
1, 2, 4, 17, 34, and 68 are 68 factors.

What are the composite factors of 68?
4, 34, and 66 are the composite 68 factors.

What are the factors of 68 in pairs?
(1, 68), (2, 34), and (4, 17) are the only pair of 68.

What are the positive factors of 68?
1, 2, 4, 17, 34, and 68 are the positive 68 factors.

What are the highest common factors of 15 and 68?
1 is the HFC between 15 and 68.

Now that you are provided with all the necessary information on factors of 68 and we hope this article is helpful to you. If you have any questions related to this page, ping us through the comment box below and we will get back to you as soon as possible.