# Factors of 119

Factors of 119 are 1, 7, 17, and 119

#### How to find factors of a number

 1.   Find factors of 119 using Division Method 2.   Find factors of 119 using Prime Factorization 3.   Find factors of 119 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 119

• Divide 119 by 1: 119 ÷ 1 : Remainder = 0
• Divide 119 by 7: 119 ÷ 7 : Remainder = 0
• Divide 119 by 17: 119 ÷ 17 : Remainder = 0
• Divide 119 by 119: 119 ÷ 119 : Remainder = 0

Hence, Factors of 119 are 1, 7, 17, and 119

#### 2. Steps to find factors of 119 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 119 using the division method, follow these steps:

• Step 1. Start dividing 119 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 119, which is 7. Divide 119 by 7 to obtain the quotient (17).
119 ÷ 7 = 17
• Step 3. Repeat step 1 with the obtained quotient (17).
17 ÷ 17 = 1

So, the prime factorization of 119 is, 119 = 7 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 119 as shown below:

So, the prime factorization of 119 is, 119 = 7 x 17.

#### 3. Find factors of 119 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 119 would be the two numbers which, when multiplied, give 119 as the result.

The following table represents the calculation of factors of 119 in pairs:

Factor Pair Pair Factorization
1 and 119 1 x 119 = 119
7 and 17 7 x 17 = 119

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 119. They are called negative pair factors.

Hence, the negative pairs of 119 would be ( -1 , -119 ) , ( -7 , -17 ) .

#### 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 119 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, 7, 17, 119 are exact divisors of 119.
• Factors of 119 are 1, 7, 17, 119. Each factor divides 119 without leaving a remainder.

• What two numbers make 119?

Two numbers that make 119 are 7 and 17.

• What is prime factorization of 119?

Prime factorization of 119 is 7 x 17.

• Write some multiples of 119?

First five multiples of 119 are 238, 357, 476, 595.

• Which is the smallest prime factor of 119?

The smallest prime factor of 119 is 7.

• Is 119 a perfect square?

No 119 is not a perfect square.

• What is the sum of all factors of 119?

The sum of all factors of 119 is 144.

• What are factors of 119?

Factors of 119 are 1, 7, 17, 119.

• How do you find factors of a negative number? ( eg. -119 )?

Factors of -119 are -1, -7, -17, -119.

• Is 119 a whole number?

Yes 119 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 119. Help him in finding the mean of 119.

Factors of 119 are 1, 7, 17, 119.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 119 is 1 + 7 + 17 + 119 = 144.
Hence, the mean of factors of 119 is 144 ÷ 4 = 36.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 119? Help her in writing all the factors.

Positive factors are 1, 7, 17, 119.
Negative factors are -1, -7, -17, -119.

Joey wants to write all the prime factors of 119 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 119 are 7, 17.
So in exponential form it can be written as 7 x 17.

Kevin has been asked to write 3 factor(s) of 119. Can you predict the answer?

3 factor(s) of 119 are 1, 7, 17.

Sammy is puzzled while calculating the prime factors of 119. Can you help him find them?

Factors of 119 are 1, 7, 17, 119.
Prime factors of 119 are 7, 17

What is prime factorization of 119?

Prime factorization of 119 is 7 x 17 = 7 x 17.

Can you help Rubel to find out the product of the even factors of 119?

Factors of 119 are 1, 7, 17, 119.
Even factors of 119 are 0.
Hence, product of even factors of 119 is; 0 = 0.