# Factors of 319

Factors of 319 are 1, 11, 29, and 319

#### How to find factors of a number

 1.   Find factors of 319 using Division Method 2.   Find factors of 319 using Prime Factorization 3.   Find factors of 319 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 319

• Divide 319 by 1: 319 ÷ 1 : Remainder = 0
• Divide 319 by 11: 319 ÷ 11 : Remainder = 0
• Divide 319 by 29: 319 ÷ 29 : Remainder = 0
• Divide 319 by 319: 319 ÷ 319 : Remainder = 0

Hence, Factors of 319 are 1, 11, 29, and 319

#### 2. Steps to find factors of 319 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 319 using the division method, follow these steps:

• Step 1. Start dividing 319 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 319, which is 11. Divide 319 by 11 to obtain the quotient (29).
319 ÷ 11 = 29
• Step 3. Repeat step 1 with the obtained quotient (29).
29 ÷ 29 = 1

So, the prime factorization of 319 is, 319 = 11 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 319 as shown below:

So, the prime factorization of 319 is, 319 = 11 x 29.

#### 3. Find factors of 319 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 319 would be the two numbers which, when multiplied, give 319 as the result.

The following table represents the calculation of factors of 319 in pairs:

Factor Pair Pair Factorization
1 and 319 1 x 319 = 319
11 and 29 11 x 29 = 319

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 319. They are called negative pair factors.

Hence, the negative pairs of 319 would be ( -1 , -319 ) , ( -11 , -29 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every number is a factor of zero (0), since 319 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, 11, 29, 319 are exact divisors of 319.
• Factors of 319 are 1, 11, 29, 319. Each factor divides 319 without leaving a remainder.

• Is 319 a perfect square?

No 319 is not a perfect square.

• What are factors of 319?

Factors of 319 are 1, 11, 29, 319.

• Which is greatest factor of 319?

The greatest factor of 319 is 29.

• What is the sum of all factors of 319?

The sum of all factors of 319 is 360.

• What are multiples of 319?

First five multiples of 319 are 638, 957, 1276, 1595.

• What is the greatest prime factors of 319?

The greatest prime factor of 319 is 29.

• What are six multiples of 319?

First five multiples of 319 are 638, 957, 1276, 1595, 1914, 2233.

• What is prime factorization of 319?

Prime factorization of 319 is 11 x 29.

• Is 319 a whole number?

Yes 319 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 319? Help her in writing all the factors.

Positive factors are 1, 11, 29, 319.
Negative factors are -1, -11, -29, -319.

Can you help Sammy find out the product of the odd factors of 319?

Factors of 319 are 1, 11, 29, 319.
Odd factors of 319 are 1, 11, 29, 319.
Hence product of odd factors of 319 is; 1 x 11 x 29 x 319 = 101761.

Joey wants to write all the prime factors of 319 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 319 are 11, 29.
So in exponential form it can be written as 11 x 29.

How many factors are there for 319?

Factors of 319 are 1, 11, 29, 319.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 319. Can you predict the answer?

3 factor(s) of 319 are 1, 11, 29.

Sammy is puzzled while calculating the prime factors of 319. Can you help him find them?

Factors of 319 are 1, 11, 29, 319.
Prime factors of 319 are 11, 29

What is prime factorization of 319?

Prime factorization of 319 is 11 x 29 = 11 x 29.