Factors of 68 – With Division and Prime Factorization

Factors Of 68

The factors of 68 are the numbers that divide 68 into a quotient that is a whole number.

An original number is divided uniformly by its factors. Multiplying the factors in pairs gives the original number as the result. The number 68 is a composite number with more than two factors, unlike prime numbers.

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

The multiples are different form factors because they are given extended times, such as 68, 136, 204, 272, 340, 408, 476, 544, 612, 680, and so on. In this article, you will discover the factors of number 68, along with its prime factorization.

What are the Factors of 68?

The factors of 68 are the numbers that divide the original number evenly. The factors in 68 are 1, 2, 4, 17, 34, and 68 in total. Each of these factors divides 68 equally.

In this case, there are more than 2 factors, thus 68 is a composite.

68 has the smallest factor of 1 and the highest factor is 68 itself.

As a result, we have evaluated only two factors of 68. The factors can also be arranged in ascending order after finding them.

In the following section, we will learn how to find the other factors.

What are the Factors of -68?

When we multiply two numbers, and we get -68 as a product, those numbers are the factors of -68.

Here is the explanation:

-1 × 68 = -68

1 × -68 = -68

-2 × 34 = -68

2 × -34 = -68

-4 × 17 = -68

4  × -17 = -68

We can get -68 by having (-1, 68), (-2, 34), and(-4, 17), as a pair of factors. Similarly, we can also get -68 by having (1, -68), (2, -34), and(4, -17) as a pair of factors.

How to Find Factors of 68?

A factor is a real number that divides the original number by itself evenly or completely. We already know that 1 is the factor of all whole numbers. In addition, a number itself is a factor. Therefore, 68 is divisible by 2, since it is an even number. As a result, the quotient we get after dividing 64 by 2 is also a factor of68.

Now let’s find out all the factors.

68 ÷ 1 = 68

68 ÷ 2 = 34

68 ÷ 4 = 17

68 ÷ 17 = 4

68 ÷ 34 = 2

68 ÷ 68 = 1

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

Factor Of 68 in Pairs

In order to find the pair factors, multiply two numbers in a pair in order to get the original number, 68, for example;

1 × 68 = 68

2 × 34 = 68

4 × 17 = 68

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

As a result, we can write the negative pair factors of 68 as the result of multiplying two negative numbers together.

-1 × -68 = 68

-2 × -34 = 68

-4 × -17 = 68

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

Factors of 68 in Ascending Order

The factors that make up the number 68 have already been gathered here, so let us arrange them in ascending order, as follows:

1<2<4<17<34<68

According to this arrangement, the smallest factor is 1 and the largest factor is 68.

Prime Factorization of 68

In mathematics, 68 is a composite number. Now, let’s determine its prime factors.

• You will need to divide the number 68 by the smallest prime factor, i.e. 2, and then divide the output by 2 again until you get a fraction or an odd number.

68 ÷ 2 = 34

• Dividing 34 by 2 again now.

34 ÷ 2 = 17

There are only two factors to the numbers 17; 1 and 17. Since 17 is a prime number, we know it is a prime number. As a result, we cannot continue to divide after 17.

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 Factorization of 68: 22 × 17
• Pair Factors of 68: (1,68), (2,34), and (4,17)
• Sum of Factors of 68: 126
• The highest factor of 68: 68
• The smallest factor of 68: 1

Solved Examples

Q.1: There are 68 pens in the room. If there are 17 baskets in the room, then how many pens can be put on each basket?

Solution:

Given

Number of pens= 68

Number of baskets in room = 17

Number of pen on each basket = 68/17 = 4

Therefore, on each basket, 4 pens can be putted.

Q.2: Add all the factors of 68 together

Solution: There are three factors in 68: 1, 7 and 68.

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

As a result, the required amount is 126.

Q.3: What is the most common factor between 60 and 68?

Solution: Let’s write down the factors of both numbers.

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Factors of 68 = 1, 2, 4, 17, 34, 68.

As a result, the greatest common factor is only 4.

FAQ`s

What are the factors of 68?

In total, there are six factors of 68. The factors are 1, 2, 4, 17, 34, and 68.

How is 68 represented as the product of prime factors?

Factorization of the number 68 is as follows:

68 = 2 × 2 × 17

Is 3 a factor of 68?

Three is not a factor of 68. There is no way to divide 68 by three.

Is 68 a prime number?

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

Is 68 a perfect square?

The root of 68 is not a whole number but an irrational number, so 68 is not a perfect square.