Factors of 51 | Division and Prime Factorization | Easy Guide

Factors Of 51

The factors of 51 are the numbers that multiply to produce the number 51. Multiply 3 by 4, for example, and we get 12, i.e., 3 × 4 = 12. Here, 3 and 4 are the factors of 12. Also, you can find the factors of 51 in a similar fashion. This article describes the factors of 51 as well as the prime factors of 51, along with steps on how to find them.

Factors of 51 are whole numbers that divide the original number uniformly or equally. This means the remainder is either none or zero after division. For instance, 8 divides 24 into 3 equal parts, factors of 24.

What are the Factors of 51?

Consequently, 51 is a composite number with more than two factors.

1, 3, 17, and 51

Furthermore, we know that 51 is divisible by its exact factors. In other words, we can find factors in different ways, such as by using a division method, factorization, and arrangements of objects.

What are the Factors of -51?

We can get -51 by having (-1, 51), (-3, 17), and (-17, 3) as a pair of factors. Similarly, we can also get -51 by having (1, -51), (3, -17), and (17, -3) as a pair of factors.

How to Find the Factors of 51?

In order to determine the factors for 51, follow these steps:

•   First, In your notebook, write the number 51.
• Multiply a number by another, such as 3 by 17, to get 51.
• 3 is a prime number whose factors are only 1 and the number itself. There is no way to factorize it further.
• 3 = 1 × 3
• You cannot factorize 17 since it is a prime number.
• 17 = 1 × 17
• As a result, 51 can be factorized into 1 × 3 × 17.

Here, we obtain unique numbers of 1, 3, 17, and 51.

Factor pairs of 51

As you know, when multiplying two numbers in a pair to get the original number, you will find the pair factors of 51. The following are some of these pair factors:

1 × 51 = 51; (1, 51)

3 × 17 = 51; (3, 17)

17 × 3 = 51; (17, 3)

51 × 1 = 51; (51, 1)

Thus, these are the positive pair factors for 51.

Therefore, the factors of 51 are 1, 3, 17, and 51.

In addition, the negative pair factors of 51 can also be written as:

(-1) × (-51) = 51

(-3) × (-17) = 51

(-17) × (-3) = 51

(-51) × (-1) = 51

In the following order, the negative pair factors of 51 are (-1, -51), (-3, -17), (-17, -3), and (-51, -1).

How to calculate Prime Factors of 51?

Similarly, Prime factors of 51 can be written using the prime factorization method.

We start by dividing the number 51 by the smallest prime number, 2.

51 ÷ 2 = 25.5

The factors of 51 cannot be fractions, so 2 is not the prime factor.

As we move forward, we have the prime numbers, i.e., 3, 5, 7, and so on.

51 ÷ 3 = 17, 3 and 17 are prime, so we cannot use the division method.

Thus, the prime factors of 51 are 3 and 17. We can also write the prime factorization of 51 as follows:

51 =  3 × 17

Similarly, the prime factors of 34 are 1, 2, 17, and 34.

Solved examples

Example 1:

Calculate the common factors of 34 and 75.

Solution:

Factors of 34: 1, 2, 17, and 34.

Factors of 75 = 1, 3, 5, 15, 25, and 75.

Therefore, 34 and 75 have a common factor of 1.

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