Factors of 119

The sum of the seven consecutive prime numbers (7, 11, 13, 17, 19, 23, and 29) is 119. Let us explore the factors of this number and different ways to find them. In this lesson, we will calculate the factors of 119, prime factors of 119, and factors of 119 in pairs along with solved examples for a better understanding.

• Factors of 119: 1, 7, 17, and 119.
• Prime Factorization of 119 : 119 = 7 × 17

What are the Factors of 119?

Factors of 119 are numbers which exactly divide it and gives the remainder as 0. So, when you multiply any two whole numbers with each other and get 119 as the answer you can say that both of those two numbers will be the factors of 119. For example, you can get 119 as an answer as:

• 1 × 119 = 119
• 7 × 17 = 119

So in general we can say that "The factors of 119 are all the integers that divide 119 without any remainder."

How to Calculate the Factors of 119?

Let's try calculating the factors of 119, starting with the smallest whole number i.e. 1. Divide 119 with this number.
Is the remainder 0?
Yes! So, we will get:

• 119 ÷ 1 = 119
• 119 × 1= 119

The next number is 7.
Now, divide 119 with this number.

• 119 ÷ 7= 17
• 17 × 7= 119

Proceeding in a similar manner we get,

• 1 × 119 = 119
• 7 × 17 = 119
• 17 × 7= 119

Hence, the factors of 119 are 1, 7, 17 and 119.

Explore factors using illustrations and interactive examples.

• Factors of 19 - The factors of 19 are 1 and 19
• Factors of 110 - The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.
• Factors of 117 - The factors of 117 are 1, 3, 9, 13, 39 and 117.
• Factors of 112 - The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

"Prime factorization means to express a composite number as the product of its prime factors."

Prime Factorization By Division

To get the prime factorization of 119, we divide it by its prime factor, say 7.

• 119 ÷ 7 = 17

Now, 17 is divided by its prime factor and the quotient is obtained.
This process goes on till we get the quotient as 1

• 17 ÷ 17 = 1

Prime Factorization By Factor Tree

We can do the same procedure using the factor tree as shown in the diagram given below:

Prime Factorization By Upside-Down Division

The prime factorization of 119 is shown below:

The prime factors of 119 are, 7 × 17

Important Notes:

• When you divide a number by its factor, the quotient of the division is also a factor.
• Factors of 119 are 1, 7, 17, and 119
• When a number is a factor of the given number, then its additive inverse is also a factor of the given number.
• For example, since 7 is a factor of 119, -7 is also a factor of 119

Factors of 119 in Pairs

The pair of numbers which gives 119 when multiplied are known as factor pairs of 119.
Following are the factors of 119 in pairs:

Observe in the table above, after 7 × 17, the factors start repeating accept the order.
So, it is enough to find factors until (7, 17)
Pairs of factors of 119 are: (1, 119), (7, 17)

Let's have a look at negative pair factors of 119. So, if we consider negative integers, then both the numbers in the pair factors will be negative.
It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.
So, we can have factor pairs of 119 as (-1, -119), (-7, -17)

Challenging Question:

• Can multiples of 119 be also factors of 119?
• What is the sum of all the factors of 119?

FAQs on Factors of 119

What are the prime factors of 119?

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

What are the positive pairs of factors of 119?

Pairs of factors of 119 are: (1, 119), (7, 17).

What are the negative pairs of factors of 119?

Pairs of factors of 119 are: (-1, -119), (-7, -17).

How many factors of 119 are there?

There are 4 factors of 119: 1, 7, 17, and 119.

What are the factors of 119?

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