# Factors of 351

Factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351

#### How to find factors of a number

 1.   Find factors of 351 using Division Method 2.   Find factors of 351 using Prime Factorization 3.   Find factors of 351 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 351

• Divide 351 by 1: 351 ÷ 1 : Remainder = 0
• Divide 351 by 3: 351 ÷ 3 : Remainder = 0
• Divide 351 by 9: 351 ÷ 9 : Remainder = 0
• Divide 351 by 13: 351 ÷ 13 : Remainder = 0
• Divide 351 by 27: 351 ÷ 27 : Remainder = 0
• Divide 351 by 39: 351 ÷ 39 : Remainder = 0
• Divide 351 by 117: 351 ÷ 117 : Remainder = 0
• Divide 351 by 351: 351 ÷ 351 : Remainder = 0

Hence, Factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351

#### 2. Steps to find factors of 351 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 351 using the division method, follow these steps:

• Step 1. Start dividing 351 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 351, which is 3. Divide 351 by 3 to obtain the quotient (117).
351 ÷ 3 = 117
• Step 3. Repeat step 1 with the obtained quotient (117).
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1

So, the prime factorization of 351 is, 351 = 3 x 3 x 3 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 351 as shown below:

So, the prime factorization of 351 is, 351 = 3 x 3 x 3 x 13.

#### 3. Find factors of 351 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 351 would be the two numbers which, when multiplied, give 351 as the result.

The following table represents the calculation of factors of 351 in pairs:

Factor Pair Pair Factorization
1 and 351 1 x 351 = 351
3 and 117 3 x 117 = 351
9 and 39 9 x 39 = 351
13 and 27 13 x 27 = 351

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 351. They are called negative pair factors.

Hence, the negative pairs of 351 would be ( -1 , -351 ) , ( -3 , -117 ) , ( -9 , -39 ) and ( -13 , -27 ) .

#### 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 351 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, 9, 13, 27, 39, 117, 351 are exact divisors of 351.
• Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351. Each factor divides 351 without leaving a remainder.

• Which is the smallest prime factor of 351?

Smallest prime factor of 351 is 3.

• Is 351 a perfect square?

No 351 is not a perfect square.

• What are five multiples of 351?

First five multiples of 351 are 702, 1053, 1404, 1755, 2106.

• What is prime factorization of 351?

Prime factorization of 351 is 3 x 3 x 3 x 13.

• What are factors of 351?

Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351.

• How do you find factors of a negative number? ( eg. -351 )?

Factors of -351 are -1, -3, -9, -13, -27, -39, -117, -351.

• Is 351 a whole number?

Yes 351 is a whole number.

• Which is greatest factor of 351?

The greatest factor of 351 is 117.

• What are the prime factors of 351?

The factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351.
Prime factors of 351 are 3, 3, 3, 13.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 351. Can you help her?

Prime factors of 351 are 3, 3, 3, 13.
Hence, the product of prime factors of 39.

Can you help Rubel to find out the product of the even factors of 351?

Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351.
Even factors of 351 are 0.
Hence, product of even factors of 351 is; 0 = 0.

Joy wants to calculate mean of all the factors of 351. Help him in finding the mean of 351.

Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 351 is 1 + 3 + 9 + 13 + 27 + 39 + 117 + 351 = 560.
Hence, the mean of factors of 351 is 560 ÷ 8 = 70.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 351? Help her in writing all the factors.

Positive factors are 1, 3, 9, 13, 27, 39, 117, 351.
Negative factors are -1, -3, -9, -13, -27, -39, -117, -351.

How many factors are there for 351?

Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351.
So there are in total 8 factors.

Joey wants to write all the prime factors of 351 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 351 are 3, 3, 3, 13.
So in exponential form it can be written as 33 x 13.

Kevin has been asked to write 7 factor(s) of 351. Can you predict the answer?

7 factor(s) of 351 are 1, 3, 9, 13, 27, 39, 117.