Factors
Factors of 107 | Prime Factorization of 107 | Factor Tree of 107
Written by Prerit Jain
Updated on: 12 Aug 2023
Contents
Factors of 107 | Prime Factorization of 107 | Factor Tree of 107
Factors of 107
| Factors of 107 | Factor Pairs of 107 | Prime factors of 107 |
| 1, 107 | (1, 107) | 107 |
Calculate Factors of
The Factors are
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What are the factors of 107
- Start by listing all of the numbers that are less than or equal to the square root of 107. The square root of 107 is about 10.3, so we can list the numbers that are less than or equal to 10.3: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
- For each of these numbers, divide 107 by the number and see if the result is a whole number. If it is, then the number is a factor of 107. If it is not, then it is not a factor of 107.
- For each factor of 107, add the number to the list of factors. For example, if 7 is a factor of 107, then we would add 7 to the list of factors.
- Repeat this process until you have found all of the factors of 107.
Using this method, the factors of 107 are 1 and 107.
How to Find Factors of 107
Given below are the methods through which you can find the factors of 107:
- Factors of 107 using the Multiplication Method
- Factors of 107 using the Division Method
- Prime Factorization of 107
- Factor tree of 107
Factors of 107 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 107 using the multiplication method, we can follow these steps:
- Start with the number 1 as a potential factor.
- Multiply 1 by different numbers and check if the result is equal to 107.
- 1 × 1 = 1 (not equal to 107)
- 1 × 2 = 2 (not equal to 107)
- 1 × 3 = 3 (not equal to 107)
- …
- 1 × 106 = 106 (not equal to 107)
- 1 × 107 = 107 (equal to 107)
- Since 1 and 107 are the only numbers that, when multiplied by 1, give the result of 107, they are the factors of 107.
Therefore, the factors of 107 found using the multiplication method are 1 and 107.
Therefore, the factors of 107 are 1 and 107.
Factors of 107 Using the Division Method
Follow the given steps below to find the factors of 107 through the division method:
- To find the factors of 107, divide it by each whole number starting with 2. If To find the factors of 107, start by dividing 107 by the smallest prime number, which is 2. If the result is a whole number, then 2 is a factor of 107. If it is not, then divide 107 by the next smallest prime number, which is 3. Continue this process until you find a prime number that is a factor of 107.
- Once you have found a prime factor of 107, divide 107 by that prime factor. If the result is a whole number, then the prime factor is a true factor of 107 and you can add it to the list of factors. If it is not, then the prime factor is not a factor of 107 and you can skip it.
- Repeat this process until you have found all of the factors of 107.
Hence, the factors of 107 are 1 and 107.
Prime Factorization of 107
Calculate Prime Factors of
The Prime Factors of 107 =
107
To find the prime factorization of 107, we need to find the prime numbers that can be multiplied together to equal 107. A prime number is a whole number greater than 1 that is only divisible by 1 and itself.
107 is a prime number, which means that it is already in its simplest form and cannot be written as the product of other prime numbers. Therefore, the prime factorization of 107 is simply 107.
Factor tree of 107
A factor tree is a way to represent the prime factorization of a number visually. It is created by dividing the number by smaller and smaller prime numbers until you reach the prime factorization.
The factor tree for 107 is shown below:
107
|
107
Since 107 is a prime number, it has only one prime factor: itself. Therefore, the factor tree for 107 consists of a single branch with 107 at the end.
Factor Pairs of 107
Calculate Pair Factors of
1 x 107=107
So Pair Factors of 107 are
(1,107)
- To find the factor pairs of 107, start by listing all of the numbers that are less than or equal to the square root of 107. The square root of 107 is about 10.3, so we can list the numbers that are less than or equal to 10.3: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
- For each of these numbers, divide 107 by the number. If the result is a whole number, then the number is a factor of 107. If it is not, then it is not a factor of 107.
- For each factor of 107, create a factor pair by combining the factor with the result of the division. For example, if 7 is a factor of 107, then we would create the factor pair (7, 15).
- Repeat this process until you have found all of the factor pairs of 107.
Using this method, we can find that the factor pairs of 107 are (1, 107) and (107, 1).
More Factors
Factors of 107 – Quick Recap
- Factors of 107: 1, 107
- Negative Factors of 107: -1, -107.
- Prime Factors of 107: 107
- Prime Factorization of 107: 107
Solved Examples of Factor of 107
Q.1: What two numbers multiplied together equal 107?
Solution: 1 × 107 = 107
Q.2: If a number is divisible by 2 and 7, what could it be?
Solution: If a number is divisible by both 2 and 7, it could be any multiple of the product of those two numbers. The product of 2 and 7 is 14. So, any multiple of 14 would be divisible by both 2 and 7. Some examples of numbers that are divisible by both 2 and 7 are: 14, 28, 42, 56, 70, and so on.
Q.3: How many times does 7 go into a number that equals 105?
Solution: 7 goes into 107, 15 times (107/7= 15)
Q.4: If you had 22 people in a room, how many more people would you need to add for the total to reach 107?
Solution: 85 people (22 + 85 =107)
Q.5: What is the prime factorization of the number 107?
Solution: The prime factorization of 107 is simply 107 itself. Since 107 is a prime number, it does not have any factors other than 1 and itself. Therefore, the prime factorization of 107 is just 107.
Q.6: What are all the even factors of 107?
Solution: Since 107 is an odd prime number, it does not have any even factors. Even factors are only possible for even numbers, as they can be divided by 2 without leaving a remainder. As 107 is not divisible by 2, it does not have any even factors.
Q.7: How many multiples of 5 are there between 105 and 115?
Solution: To find the number of multiples of 5 between 105 and 115, we can check which numbers within that range are divisible by 5. The multiples of 5 in the given range are 105, 110, and 115. Therefore, there are 3 multiples of 5 between 105 and 115.
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Frequently Asked Questions on Factors of 107
What are the factors of 107?
The factors of 107 are 1 and 107.
Is 107 a prime number?
No, 107 is a prime number as it has factors (1 and 107) only.
Is there an even factor of 107?
No, there is no even factor of 107.
How many times does 7 go into 107?
Dividing 107 by 7 gives us a quotient of 15 with a remainder of 2. Therefore, 7 goes into 107 exactly 15 times with a remainder of 2.
What is the prime factorization of the number 107?
Since 107 is a prime number, it does not have any factors other than 1 and itself. Therefore, the prime factorization of 107 is just 107.13.
Can you divide 107 by 2 and 7?
No, we cannot divide 107 by 2 and 7 without any remainders since it’s not divisible by both numbers.
Find a minimum three-digit number that has 107 as its factor.
The closest multiple of 107 within the three-digit range is 107 itself. Since 107 is a three-digit number and it is divisible by 107, it meets the criteria.
How many multiples of 5 are there between 105 and 115?
There are 3 multiples of 5 between 105 and 115; namely 105, 110, and 115.
How many odd factors does 107 have?
There are 2 odd factors of 107; namely 1 and 107.
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