Factors of 83 Using Prime Factorization
What are the Factors of 83?
The natural numbers that can divide 83 evenly are known as the factors of 83. When 83 is divided by its factor, the remainder is zero, and the quotient is also a factor of 83.
The number 83 has a total of two factors: 1, 83.
Factors | Factor Pair | Prime Factorization |
|---|---|---|
1 , 83 | (1, 83) | 1 x 83 |
Factor List of the Number 83
The factors of 83 can be obtained using divisibility rules and division facts.
Number | Is the number a factor of 83? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all numbers | 1 x 83 = 83 |
2 | No, 83 is an odd number | --- |
3 | No, 8 + 3 = 11 is not divisible by 3 | --- |
4 | No, 83 \(\div\) 4 = 20 Remainder = 3 | --- |
5 | No, the ones digit is neither 0 nor 5 | --- |
6 | No, 83 is neither even nor divisible by 3 | --- |
7 | No, 83 \(\div\) 11 = 7 and Remainder = 6 | --- |
8 | No, 83 \(\div\) 8 = 10 and Remainder = 3 | --- |
9 | No, Since 83 is not divisible by 3 | --- |
10 | No, 83 \(\div\) 10 = 8 and Remainder = 3 | --- |
11 | No, 83 \(\div\) 11 = 7 and Remainder = 6 | --- |
So 83 has exactly two factors, 1 and 83 itself so 83 is a prime number.
[Note: To determine whether a number is a factor of 83 or not, divide 83 by that number and check whether the remainder is zero or not. If the remainder is zero then the number is a factor of 83.]
Prime Factors of 83
The factor tree below depicts the prime factorization of the number 83.
So the prime factorization of 83 is given by 1 x 83 and the prime factor of 83 is the number (83) itself.
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Factor Pairs of 83
A factor pair of 83 is a set of two factors of 83, such that their product is 83. A number can have a positive pair of factors and a negative pair of factors.
For example, (1, 83) is a factor pair of 83 as,
1 x 83 = 83
Positive factor pair of 83:
Positive factors of 83 | Positive factor pair of 83 |
|---|---|
1 x 83 = 83 | (1, 83) |
So, the factor pair for 83 is (1, 83) or (83, 1).
Solved Factors of 83 Examples
Example 1: Find the sum and average of factors of 83.
Solution:
The factors of 83 are : 1 and 83.
Sum of factors of 83 = 1 + 83 = 84
Total number of factors = 2
Average of factors = \(\frac{\text{Sum of factors}}{\text{total number of factors}}=\frac{84}{2}=42\)
Hence, the sum and average of the factors of 83 is 84 and 42 respectively.
Example 2 : Find the greatest common factor of 83 and 85.
Solution:
To find the greatest common factor of 83 and 85, list the factors of 83 and 85 and select the highest common factor.
Factors of 83 : 1, 83
Factors of 85 : 1, 5, 17, 85
The only common factor of 83 and 85 is 1
Therefore, the greatest common factor of 83 and 85 is 1.
Example 3: A contractor buys 83 solar panels. He wants to organize the panels into a rectangular array. How many different arrays can he make?
Solution:
To find the number of arrays the contractor can make, find the number of factor pairs of 83
There is only one factor pair for 83: (1, 83)
You can use this factor pair to make 2 arrays, that is, as (1, 83) and as (83, 1).
So there are 1 x 2 = 2 ways to organize the panels in different arrays.
If the number has factors other than 1 and the number itself, it will be a composite number. In other words, composite numbers have more than two factors.
Factors of 83: 1, 83
Since 83 does not have factors other than 1 and itself (83) so 83 is not a composite number.
When we divide 83 by 7 we get 11 as the quotient and 6 as the remainder, that is, remainder is not zero. So 7 does not divide 83 evenly. Therefore 7 is not a factor of 83.
A number which has only two factors that is 1 and the number itself is known as a prime number.