# Factors of 51

Factors of 51 are 1, 3, 17, and 51

#### How to find factors of a number

 1.   Find factors of 51 using Division Method 2.   Find factors of 51 using Prime Factorization 3.   Find factors of 51 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 51

• Divide 51 by 1: 51 ÷ 1 : Remainder = 0
• Divide 51 by 3: 51 ÷ 3 : Remainder = 0
• Divide 51 by 17: 51 ÷ 17 : Remainder = 0
• Divide 51 by 51: 51 ÷ 51 : Remainder = 0

Hence, Factors of 51 are 1, 3, 17, and 51

#### 2. Steps to find factors of 51 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 51 using the division method, follow these steps:

• Step 1. Start dividing 51 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 51, which is 3. Divide 51 by 3 to obtain the quotient (17).
51 ÷ 3 = 17
• Step 3. Repeat step 1 with the obtained quotient (17).
17 ÷ 17 = 1

So, the prime factorization of 51 is, 51 = 3 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 51 as shown below:

So, the prime factorization of 51 is, 51 = 3 x 17.

#### 3. Find factors of 51 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 51 would be the two numbers which, when multiplied, give 51 as the result.

The following table represents the calculation of factors of 51 in pairs:

Factor Pair Pair Factorization
1 and 51 1 x 51 = 51
3 and 17 3 x 17 = 51

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 51. They are called negative pair factors.

Hence, the negative pairs of 51 would be ( -1 , -51 ) , ( -3 , -17 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 51 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 17, 51 are exact divisors of 51.
• Factors of 51 are 1, 3, 17, 51. Each factor divides 51 without leaving a remainder.

• How do you find factors of a negative number? ( eg. -51 )?

Factors of -51 are -1, -3, -17, -51.

• What is the sum of all factors of 51?

The sum of all factors of 51 is 72.

• What is prime factorization of 51?

Prime factorization of 51 is 3 x 17.

• What are the pair factors of 51?

Pair factors of 51 are (1,51), (3,17).

• What are six multiples of 51?

First five multiples of 51 are 102, 153, 204, 255, 306, 357.

• Is 51 a whole number?

Yes 51 is a whole number.

• Which is the smallest prime factor of 51?

Smallest prime factor of 51 is 3.

• What are five multiples of 51?

First five multiples of 51 are 102, 153, 204, 255, 306.

• Write all factors of 51?

Factors of 51 are 1, 3, 17, 51.

#### Examples of Factors

Joey wants to write all the prime factors of 51 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 51 are 3, 17.
So in exponential form it can be written as 3 x 17.

How many factors are there for 51?

Factors of 51 are 1, 3, 17, 51.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 51. Can you predict the answer?

3 factor(s) of 51 are 1, 3, 17.

Sammy is puzzled while calculating the prime factors of 51. Can you help him find them?

Factors of 51 are 1, 3, 17, 51.
Prime factors of 51 are 3, 17

What is prime factorization of 51?

Prime factorization of 51 is 3 x 17 = 3 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 51. Can you help her?

Prime factors of 51 are 3, 17.
Hence, the product of prime factors of 51.

Can you help Rubel to find out the product of the even factors of 51?

Factors of 51 are 1, 3, 17, 51.
Even factors of 51 are 0.
Hence, product of even factors of 51 is; 0 = 0.