Factors of 119

The numbers that divide 119 evenly are known as factors of 119. A factor of 119 is a number that divides the number without remainder. The factors of 119 are 1, 7, 17, and 119.

Negative factors of 119: -1, -7, -17, and -119.

Prime factors of 119: 7 and 17.

Prime factorization of 119: 7 × 17.

The sum of factors of 119: 1 + 7 + 17 + 119 = 144

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 119. Identifying the numbers which are multiplied to get the number 119 is the multiplication method.

Step 1: Multiply 119 by 1, 119 × 1 = 119.

Step 2: Check for other numbers that give 119 after multiplying 7 × 17 = 119

Therefore, the positive factor pairs of 119 are: (1, 119) and (7, 17). All these factor pairs result in 119. For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 119 by 1, 119 ÷ 1 = 119.

Step 2: Continue dividing 119 by the numbers until the remainder becomes 0.

119 ÷ 1 = 119

119 ÷ 7 = 17

119 ÷ 17 = 7

Therefore, the factors of 119 are: 1, 7, 17, 119.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 119 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

119 ÷ 7 = 17

17 ÷ 17 = 1

The prime factors of 119 are 7 and 17. The prime factorization of 119 is: 7 × 17.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 119 is divided by 7 to get 17.

Step 2: Now divide 17 by 17 to get 1. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 119 is: 7 × 17.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 119: (1, 119) and (7, 17).
• Negative factor pairs of 119: (-1, -119) and (-7, -17).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 119 are 1, 7, 17, and 119.

• Prime factors: The factors which are prime numbers. For example, 7 and 17 are prime factors of 119.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 119 are (1, 119) and (7, 17).

• Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the number. For example, 7 × 17 = 119.

• Prime factorization: The process of expressing a number as a product of its prime factors. For example, 119 is expressed as 7 × 17.