Factors of 109 | Prime Factorization of 109 | Factor Tree of 109

Factors of 109

Factors of 109	Factor Pairs of 109	Prime factors of 109
1, 109	(1, 109)	109

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What are the factors of 109

1. Begin by listing the factors of 109 that are less than or equal to the square root of 109. The square root of 109 is approximately 10.4, so we can list the factors of 109 that are less than or equal to 10.4: 1, 3, 7, and 10.
2. For each of these factors, divide 109 by the factor and see if the result is a whole number. If it is, then the factor is a true factor of 109. If it is not, then it is not a factor of 109.
3. For each true factor of 109, add the factor and the result of the division to the list of factors. For example, if 7 is a true factor of 109, then we would add both 7 and 15 to the list of factors.
4. Repeat this process until you have found all of the factors of 109.

Therefore, the factors of 109 are 1 and 109.

How to Find Factors of 109

The major methods to find the factors of 109 are: 

1. Factors of 109 using the Multiplication Method
2. Factors of 109 using the Division Method
3. Prime Factorization of 109
4. Factor tree of 109

Factors of 109 Using the Multiplication Method

The multiplication method is a way to find the factors of a number by multiplying pairs of numbers together. To find the factors of 109 using the multiplication method, we can follow these steps:

1. tart with the number 1 as a potential factor.
2. Multiply 1 by different numbers and check if the result is equal to 109.
   • 1 × 1 = 1 (not equal to 109)
   • 1 × 2 = 2 (not equal to 109)
   • 1 × 3 = 3 (not equal to 109)
   • …
   • 1 × 108 = 108 (not equal to 109)
   • 1 × 109 = 109 (equal to 109)
3. Since 1 and 109 are the only numbers that, when multiplied by 1, give the result of 109, they are the factors of 109.

Therefore, the factors of 109 found using the multiplication method are 1 and 109.

Factors of 109 Using the Division Method

The division method is a way to find the factors of a number by dividing the number by smaller and smaller numbers until we reach the prime factorization. To find the factors of 109 using the division method, we can follow these steps:

1. Begin by dividing 109 by the smallest prime number that is less than or equal to the square root of 109. The square root of 109 is about 10.4, and the smallest prime number that is less than or equal to 10.4 is 2. When we divide 109 by 2, we get a result of 54 with a remainder of 1. This means that 2 is not a factor of 109.
2. Next, we can try dividing 109 by the next smallest prime number, which is 3. When we divide 109 by 3, we get a result of 36 with a remainder of 1. This means that 3 is not a factor of 109.
3. We can continue this process, dividing 109 by the next smallest prime numbers (5, 7, 11, etc.) until we find a prime number that is a factor of 109.
4. Once we have found a factor of 109, we can divide 109 by that factor to find the other factor. In this case, we would divide 109 by 7 to get a result of 15.
5. We can then repeat this process until we reach the prime factorization.

Using the division method, we can find that the factors of 109 are 1 and 109. 

Prime Factorization of 109

The prime factorization of 109 is the expression of 109 as the product of its prime factors. To find the prime factorization of 109, we can follow these steps:

1. Start with the number 109.
2. Begin dividing 109 by the smallest prime numbers (2, 3, 5, 7, 11, …) until the quotient is no longer divisible evenly.
   • 109 ÷ 2 = 54.5 (not divisible by 2)
   • 109 ÷ 3 = 36.333 (not divisible by 3)
   • 109 ÷ 5 = 21.8 (not divisible by 5)
   • 109 ÷ 7 = 15.571 (not divisible by 7)
   • 109 ÷ 11 = 9.909 (not divisible by 11)
   • 109 ÷ 13 = 8.385 (not divisible by 13)
   • …
3. Since 109 is not divisible by any prime numbers smaller than itself, the prime factorization of 109 is simply 109.

Therefore, the prime factorization of 109 is 109 itself, as 109 is a prime number and has no other prime factors.

Factor tree of 109

Since 109 is a prime number, it means it cannot be factored into smaller whole numbers. Therefore, the factor tree of 109 would consist of a single node with the number 109. This indicates that 109 is a prime number and has no other factors apart from 1 and 109 itself.

In summary, the factor tree of 109 would look like this:

109

The single node represents the number 109, indicating that 109 is a prime number and cannot be further factored in.

Factor Pairs of 109

A factor pair is a set of two numbers that can be multiplied together to equal a given number. For example, the factor pairs of 15 are (1, 15), (3, 5), and (5, 3) because 1 x 15 = 15, 3 x 5 = 15, and 5 x 3 = 15.

The factor pair of 109 are (1, 109) because 1 x 109 = 109.

To find the factor pairs of a number, we can start by listing out all the factors of the number. For example, the factors of 15 are 1, 3, 5, and 15. We can then pair them up in different combinations to find all the factor pairs. For example, the factor pairs of 15 are (1, 15), (3, 5), and (5, 3).

It’s important to remember that the order of the numbers in a factor pair doesn’t matter. For example, (3, 5) and (5, 3) are both factor pairs of 15, even though the numbers are listed in different order.

More Factors

• Factors of 106
• Factors of 107
• Factors of 108
• Factors of 109
• Factors of 110
• Factors of 111
• Factors of 112

Factors of 109 – Quick Recap

• Factors of 109: 1, 109
• Negative Factors of 109: -1, -109.
• Prime Factors of 109: 109
• Prime Factorization of 109:  109

Also Check: Multiples, Square Root, and LCM

Solved Examples of Factor of 109

Q.1: What two numbers multiplied together equal 109?
Solution: 1 × 109 = 109

Q.2: If a number is divisible by 2 and 7, what could it be?
Solution: To find all the possible numbers that satisfy this condition, you can multiply 2 and 7 together, resulting in 14. So, any multiple of 14 would be divisible by both 2 and 7. Some examples of numbers that meet this criterion include 14, 28, 42, 56, and so on.

Q.3: If you had 22 people in a room, how many more people would you need to add for the total to reach 109?
Solution: 85 people (22 + 85 =109)

Q.4: What is the prime factorization of the number 109?
Solution: Prime factorization of 109 is 1 x 109.

Q.5: What three-digit number has 109 as its factor?
Solution: A three-digit number that has 109 as its factor is 109. Since 109 is a prime number, it only has two factors: 1 and 109. As a result, any three-digit number that has 109 as its factor must be 109 itself.

Q.6: What are all the even factors of 109?
Solution: Since 109 is an odd prime number, it does not have any even factors. Even factors are numbers that are divisible by 2, resulting in a whole number. Since 109 is not divisible by 2, it does not have any even factors. Therefore, the set of even factors of 109 is empty.

Q.7: How many multiples of 5 are there between 105 and 115?
Solution: There are 3 multiples of 5 between 105 and 115; namely 105, 110, and 115.

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Frequently Asked Questions on Factors of 109