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What are the Factors of 51?

Factoring Method

Last updated date: 28th Jan 2023
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Factoring is the process of looking for factors in a mathematical expression to make it look like a multiplication problem. Factoring works by reversing the multiplication process. Finding two numbers to multiply to produce another number is as simple as factoring. The six factoring methods are as follows:

  • Greatest Common Factor (GCF)

  • Grouping Method.

  • Sum or difference in two cubes.

  • The difference in the two squares method.

  • General trinomials.

  • Trinomial method.


What are the Factors of 51?

The factors of 51 and the prime factors of 51 differ because fifty-one is a composite number. The prime factors of 51 and the prime factorization of 51, despite their close relationship, are not identical. All factors of 51 are 51, 17, 3, and 1 respectively. These are all the 51 factors, and each one of them may divide 51 without rest (modulo 0). As a result, the terms 51 factors and divisors of 51 are interchangeable. The number itself, in this case, 51, as well as 1 are factors and divisors of 51, as is the case with any natural number greater than zero. We also know that the factors of 51 are the number's exact divisors.


As a result, we may obtain the factors for any number in several ways, such as using the division method, factorization, or arranging objects in specific patterns.


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Factors of 51 in Pairs


How to Find the Factors of 51?

There are 5 steps to find the factors for 51 are as follows:

  • Step 1: Write down the number 51 in your notebook.

  • Step 2: Find the two numbers that, when multiplied together, equal 51, such as 3×17 = 51.

  • Step 3: We know that 3 is a prime number, meaning it has only two factors: 1 and itself. As a result, we are unable to factorise it further.

1×3 = 3

  • Step 4: 17 is also a prime number, which means it cannot be factored.

1×17 = 17

  • Step 5: Hence, the factorization of 51 gives us 1 × 3 × 17.

Therefore, all factors of 51 are 1, 3, 17, 51.


Now here is list the factors of 51 is as follows,


Factor of 51

1

3

17

51


How to Find Factor Pairs of 51?

To calculate the factor pairs of 51, multiply the two numbers in a pair until the result is 51. The following are some examples of such numbers:

  • 1 × 51 = 51; (1, 51)

  • 3 × 17 = 51; (3, 17)

  • 17 × 3 = 51; (17, 3)

  • 51 × 1 = 51; (51, 1)

These are the (+ve) positive pair factors for the number 51.

 

Hence, all positive factors of 51 are 1, 3, 17 and 51.

 

We can also write the negative pair factors of 51 as follows:

  • (-1) × (-51) = 51

  • (-3) × (-17) = 51

  • (-17) × (-3) = 51

  • (-51) × (-1) = 51

Therefore, the (-ve) negative pair factors for the number 51 are (-1, -51), (-3, -17), (-17, -3), and (-51, -1).


Factor Tree of 51

The prime factors of number 51 are 3 and 17. It is the list of the integer's prime factors. The number of prime factors of 51 is 2 (two).

As 51 is a composite number, we can draw a factor tree of 51:


Image:


Prime Factors of 51

The prime factors of 51 are the prime numbers that divide 51 perfectly, without remainder, according to the Euclidean division rule. To put it another way, a prime factor of 51 divides the integer 51 modulo 0 without any rest. 


For 51 numbers, the prime factors are 3 and 17. By using the definition, 1 is not a prime number.


Apart from 1, the word "prime" separates the factors and prime factors of the number 51. The first list includes both composite and prime numbers, while the second list only contains prime numbers.


Prime Factorization of 51

51 has a prime factorization of 3 x 17. This is a unique list of prime factors and their multiplicities. It's important to note that while the prime factorization of 51 excludes the number 1, it does include every instance of a certain prime factor. The number 51 is composite. In contrast to prime numbers, which have only one factorization, composite numbers, such as 51, have at least two.


To see what this implies, take the rightmost and leftmost integers in 51, 17, 3, 1, then multiply them to get 51. This is the initial step in the factorization process. The second factorization, which similarly yields 51, is obtained by selecting the second rightmost and second leftmost values.


Finding the set of prime numbers that, when multiplied together, yield the original number 51 is known as prime factorization or integer factorization of 51. Prime decomposition of 51 is another name for this.


Practise Question MCQs

1. 51 is a _____

  1. Odd number

  2. Prime number

  3. Composite number

  4. Both A and C

Ans: D


2. The prime factors of a composite number 51 are

  1. 1

  2. 3,17

  3. Both A and B

  4. 511

Ans: B


Conclusion

In this article, we have learned to calculate the factors of 51, prime factors of 51, and factors of 51 in pairs along with some of the solved examples for a better understanding.

FAQs on What are the Factors of 51?

1. What are the multiples of 51?

The multiples of 51 are 51, 102, 153, 204, 255, 306, 357, 408, 459 and so on.

2. What are the common factors of 51 and 14?

The common factors of 51 numbers are 1, 3, 17, 51. And the common factors of 14 numbers are 1, 2, 7, 14.

3. what is factorisation in mathematics?

Factorization (or factorisation, see English spelling changes) or factoring is the process of representing a number or other mathematical object as the product of numerous factors, which are usually smaller or simpler things of the same kind. For example, the integer 15 is factored by 3 × 5, and the polynomial x2 - 4 is factored by (x – 2)(x + 2).

4. What are the 6 types of factoring?

The six methods are as follows:

  • Greatest Common Factor (GCF)

  • Grouping Method.

  • Sum or difference in two cubes.

  • The difference in the two squares method.

  • General trinomials.

  • Trinomial method.

5. What is meant by the prime factorization method?

A number can be expressed as a product of its prime factors using prime factorization. A prime number is one with only two factors: one and the number itself. Look at the number 30 as an example. Although we know that 30 equals 5 × 6, 6 is not a prime number. Since 3 and 2 are prime numbers, the number 6 is written as 2 × 3. As a result, 30's prime factorization is 2 × 3 × 5.

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