Factors of 119 | Prime Factorization of 119 | Factor Tree of 119

Factors of 119

Factors of 119	Factor Pairs of 119	Prime factors of 119
1, 7, 17 and 119	(1, 119) and (7, 17)	7 × 17

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What are the factors of 119

The factors of a given number can divide that given number entirely with zero decimal points in the quotient. To find the factors of 119, we can start by dividing 119 by 2. If 119 is evenly divisible by 2, then 2 is a factor of 119. If 119 is not evenly divisible by 2, then we can try dividing it by 3, and so on. 

Here’s how it would work:
119 / 2 = 59.5 (not evenly divisible)
119 / 3 = 39.67 (not evenly divisible)
119 / 4 = 29.75 (not evenly divisible)
119 / 5 = 23.8 (not evenly divisible)

We can keep going like this until we find a number that 119 is evenly divisible by. But if we keep going, we will eventually find that 119 is evenly divisible by 1 and 119.

So, the factors of 119 are 1 and 119.

How to Find Factors of 119

The most widely used methods for finding the factors of a given number are given below and through those methods, you can find the factors of 119 also. 

• Factors of 119 using the Multiplication Method
• Factors of 119 using the Division Method
• Prime Factorization of 119
• Factor tree of 119

Factors of 119 Using the Multiplication Method

To find the factors of 119 using the multiplication method, we can look for pairs of numbers that can be multiplied together to give us 119. For example, we know that 1 x 119 is equal to 119, so 1 and 119 are both factors of 119.

This means that if we multiply 1 and 119 together, we get 119. In other words, 1 and 119 are two numbers that “fit together” to make 119.

However, there are no other pairs of numbers that multiply to give us 119, so 1 and 119 are the only factors of 119 using the multiplication method.

Factors of 119 Using the Division Method

To find the factors of 119 using the division method, we can start by trying to divide 119 by different numbers. If 119 is evenly divisible by a number, then that number is a factor of 119.

For example, if we divide 119 by 2, we get 59.5. This is not a whole number, so 2 is not a factor of 119. If we divide 119 by 3, we get 39.66666666666667. This is not a whole number, so 3 is not a factor of 119.

We can keep going like this until we find all the factors of 119. In this case, there are only 2 factors of 119: 1 and 119. These are the only two numbers that, when we divide 119 by them, we get a whole number.

Prime Factorization of 119

In prime factorization, we try to express a number as a product of its prime factors. A prime number is a number that is only divisible by 1 and itself. For example, the first few prime numbers are 2, 3, 5, 7, 11, and 13.

To find the prime factorization of 119, we can start by dividing 119 by the smallest prime number, which is 2. If 119 is evenly divisible by 2, then we can divide it by 2 again and again until we get a number that is not evenly divisible by 2.

For example, if we divide 119 by 2, we get 59.5. This is not evenly divisible by 2, so we stop here.

Since 119 is not evenly divisible by 2, we move on to the next smallest prime number, which is 3. If we divide 119 by 3, we get 39.67. This is not a whole number, so 3 is not a factor of 119.

We can keep going like this until we find all the prime factors of 119. This means that the prime factors of 119 are 1 and 119, and 1 appears once in the prime factorization.

Therefore, the prime factorization of 119 is 1 x 119.

Factor tree of 119

A factor tree is a diagram that shows the prime factorization of a number. It is called a tree because it has branches that represent the different prime factors of the number.

To create a factor tree for 119, we can start by finding two numbers whose product is 119. For example, we can find that 1 and 119 are both factors of 119 because 1 x 119 = 119.

Since 1 and 119 are both prime numbers, we don’t need to find any more factors. This means that the factor tree for 119 is very simple:

Copy code

119 / \ 1 119

This diagram shows that 119 can be expressed as a product of its prime factors: 1 x 119.

In other words, if we multiply 1 and 119 together, we get 119. These are the two numbers that “fit together” to make 119.

Factor Pairs of 119

The factor pairs of a number are all the pairs of numbers that, when multiplied together, give that number. For example, the factor pairs of 12 are (1, 12), (2, 6), and (3, 4), because the product of these pairs is 12.

To find the factor pairs of 119, we can think about which numbers “fit together” to make 119. We know that 1 and 119 are both factors of 119 because 1 x 119 = 119.

So, the factor pairs of 119 are (1, 119) and (119, 1). These are the pairs of numbers that, when multiplied together, give us 119.

More Factors

• Factors of 116
• Factors of 117
• Factors of 118
• Factors of 119
• Factors of 120
• Factors of 121
• Factors of 122

Factors of 119 – Quick Recap

• Factors of 119:  1, 7, 17, and 119.
• Negative Factors of 119:  -1, -7, -17, and -119
• Prime Factors of 119: 7 x 17.
• Prime Factorization of 119:  7 x 17.

Solved Examples of Factor of 119

Q.1: Two people are playing a game and have 118 dice between them. How many dice will each player get?
Solution: Each player will get 59 dice.

Q.2: If there are 119 pages in a book, how long would it take to read if it takes an average of 2 minutes per page? 
Solution: 119 pages x 2 minutes per page = 238 minutes. Therefore, it would take approximately 238 minutes to read a 119-page book at an average pace of 2 minutes per page.

Q.3: A school wants to give away 119 pencils evenly among 8 students – how many pencils will each student receive? 
Solution: 119 pencils ÷ 8 students = 14 pencils with a remainder of 7. So, each student will receive 14 pencils, and there will be 7 pencils left over.

Q.4: How many coins should each person get if they were split among seven people with a total of 115 coins?  
Solution: 119 coins ÷ 7 people = 17 coins per person. Each person should receive 15 coins in this situation.

Q.5: What are the least prime numbers needed to multiply together in order to get 1197? 
Solution: The prime factorization of 1197 is: 1197 = 3 × 3 × 7 × 19. The least prime numbers that can be multiplied together to equal 1197 are 3 and 399.

Q.6: How many customers can buy books if there are 119 books for sale and three customers want to purchase them?  
Solution: 119 books ÷ 3 customers = 39 books per customer. Therefore, each customer can buy 39 books.

Q.7: Is 119 a prime number?  
Solution: No, 119 is not a prime number because it can be divided evenly by more than two numbers (1, 7, 17, and 119).

Q.8: What is the greatest common factor between 1185 and 1209?  
Solution: 1185 = 3 * 3 * 5 * 7 * 3 , 1209 = 3 * 13 * 31. Now, let’s identify the common prime factors between the two numbers, which are 3: Greatest Common Factor (GCF) = 3.

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Frequently Asked Questions on Factors of 119