The factors of 215 are the numbers, that produce the result as 215 when a particular pair of factors are multiplied together. These factors are 1, 5, 43 and 215. To find the factors of a number, 215, we will use the factorization method. In the factorization method, first take the numbers, 1 and 215 as factors of 215 and proceed with finding the other pair of multiples of 215 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 215 in pairs and also the prime factorization method to find the prime factors of 215 is discussed.
Table of Contents:
- What are the Factors of 215?
- Pair Factors of 215
- Factors of 215 by Division Method
- Prime Factorization of 215
- Examples
- FAQs
What are the Factors of 215?
The factors of 215 are the numbers that divide 215 exactly without leaving a remainder. As the number 215 is a composite number, it has more factors other than 1 and 215. We can say, 215 is an odd composite number. Hence, the factors of 215 are 1, 5, 43 and 215. Similarly, the negative factors of 215 are -1, -5, -43 and -215.
Factors of 215: 1, 5, 43 and 215. Prime Factorization of 215: 5 × 43 (or) 5^{1} × 43^{1}. |
Pair Factors of 215
To find the pair factors of 215, multiply the two numbers in a pair to get the original number as 215. The pair factors of 215 can be positive or negative, but they cannot be decimal or fraction. Thus, the positive and negative pair factors of 215 are given below:
Positive Pair Factors of 215:
Positive Factors of 215 |
Positive Pair Factors of 215 |
1 × 215 |
(1, 215) |
5 × 43 |
(5, 43) |
Negative Pair Factors of 215:
Negative Factors of 215 |
Negative Pair Factors of 215 |
-1 × -215 |
(-1, -215) |
-5 × -43 |
(-5, -43) |
Factors of 215 by Division Method
We know that the factors of a number can be found using two different methods, such as the division method and the prime factorization method. Now, let us first start with the division method.
In the division method, the number 215 is divided by different consecutive integers. If the integer divides 215 completely and leaves the remainder 0, then the integers are the factors of 215. Go through the following procedure to find the factors of 215.
- 215/1 = 215 (Factor is 1 and remainder is 0)
- 215/5 = 43 (Factor is 5 and remainder is 0)
- 215/43 = 5 (Factor is 43 and remainder is 0)
- 215/215 = 1 (Factor is 215 and remainder is 0)
If we divide 215 by any numbers other than 1, 5, 43 and 215, it leaves the remainder of some value. Hence, the factors of 215 are 1, 5, 43 and 215.
Prime Factorization of 215
In the prime factorization of 215, the number 215 is written as the product of its prime factors. Go through the following steps to find the prime factors of 215.
Let us take the number 215 and its pair factors as (1, 215).
We know that 215 is an odd composite number and it can be split further into its prime factors.
Thus, 215 is written as the product of 5 and 43.
Now, both the numbers 5 and 43 are prime factors and it cannot be further factored.
Thus, 215 is written as the product of 1, 5 and 43.
(i.e.) 215 = 1× 5 × 43
Hence, the prime factorization of 215 is 5×43 or 5^{1} × 43^{1}.
It is possible to find the exact number of factors of a number 215 with the help of prime factorisation. The prime factor of the 215 is 5 x 43. The exponents in the prime factorisation are 1, and 1. Add the number 1 with the exponents and multiply it. (1+1)(1+1) =2 x 2= 4. Therefore, the number 215 has 4 factors.
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Examples
Example 1:
Find the common factors of 215 and 214.
Solution:
The factors of 215 are 1, 5, 43 and 215.
The factors of 214 are 1, 2, 107 and 214.
Hence, the common factor of 215 and 214 is 1.
Example 2:
Find the common factors of 215 and 216.
Solution:
Factors of 215 = 1, 5, 43 and 215.
Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.
The common factor of 215 and 216 is 1 only.
Example 3:
Find the common factors of 215 and 43.
Solution:
The factors of 215 are 1, 5, 43 and 215.
The factors of 43 are 1 and 43.
Therefore, the common factors of 215 and 43 are 1 and 43.
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Frequently Asked Questions on Factors of 215
What are the factors of 215?
The factors of 215 are 1, 4, 53 and 215.
What is the prime factorization of 215?
The prime factorization of 215 is 5×43 or 5^{1} × 43^{1}.
What are the positive and negative pair factors of 215?
The positive pair factors of 215 are (1, 215) and (5, 43)
The negative pair factors of 215 are (-1, -215) and (-5, -43)
Mention the prime factors of 215.
The prime factors of 215 are 5 and 43.
Is 20 a factor of 215?
No, 20 is not a factor of 215. If 20 divides 215, it leaves a remainder, and hence 20 is not a factor of 215.