Factors of 58 Using Prime Factorization
What are the Factors of 58?
If the number 58 is divided by a natural number such that the remainder is zero, the natural number is known as a factor of 58. Here, the quotient obtained on division is also a factor of 58.
The factors of 58 are 1, 2, 29 and 58 because all these numbers divide the number 58 evenly.
Deriving Factor List for 58
Divisor | Is the Number a Factor of 58 | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 58 = 58 |
2 | Yes, 58 is even | 2 x 29 = 58 |
3 | No, 5 + 8 = 13 is not divisible by 3 | - |
4 | No, 58 \(\div\) 4 = 14 R2 | - |
5 | No, ones digit is neither 0 nor 5 | - |
6 | No, 58 is even but not divisible by 3 | - |
7 | No, 58 \(\div\) 7 = 8R2 | - |
8 | No, 58 \(\div\) 8 = 7R2 | - |
9 | No, 58 \(\div\) 9 = 6 R4 | - |
So, the factors of 58 are 1, 2, 29, and 58.
Prime Factorization of 58
The process of expressing 58 as the product of its prime factors is called the prime factorization of 58. 58 is a composite number, hence it has factors other than 1 and itself. To obtain the prime factorization of 58, we divide 58 by its prime factors till we get the result as 1.
Factor tree of 58 can be written as:
So, the prime factorization of 58 is 58 = 2 x 29.
Factor Pairs of 58
The factor pairs of 58 are a pair of factors of 58 which when multiplied together result in 58.
The positive factor pairs of 58 are (1, 58) and (2, 29).
1 x 58 = 58
2 x 29 = 58
Read More:
Positive Factor Pairs of 58
Positive Factors of 58 | Positive Factor Pairs of 58 |
|---|---|
1 x 58 | (1, 58) |
2 x 29 | (2, 29) |
Solved Factors of 58 Examples
Example 1: Find the common factors of 58 and 60.
Solution:
Factors of 58 = 1, 2, 29 and 58.
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Therefore, the common factors of 58 and 60 are 1 and 2.
Example 2: Find the greatest common factor of 57 and 58.
Solution:
To find the greatest common factor between 57 and 58, let’s first find the common factors between 57 and 58.
Factors of 57 = 1, 3, 19 and 57.
Factors of 58 = 1, 2, 29 and 58.
1 is the only common factor of 57 and 58.
Therefore, the greatest common factor of 57 and 58 is 1.
Example 3: Find the sum of all the factors of 58.
Solution:
Factors of 58 = 1, 2, 29 and 58.
Sum of factors = 1 + 2 + 29 + 58 = 90.
So, the sum of all the factors of 58 is 90.
Example 4: Lorie has 58 pots of plants that she wants to place in her backyard. She decides to arrange them in rows such that each row has an equal number of pots. Can you show her the different ways in which she can place the pots?
Solution :
Number of pots = 58
The number of pots in each row should be equal.
Therefore, Number of pots in each row x Number of rows = 58
The possible combinations are:
Number of pots in each row | Number of rows |
|---|---|
1 | 58 |
2 | 29 |
29 | 2 |
58 | 1 |
No, 58 is even but not divisible by 3. If we divide 58 by 6 then we get 9 as quotient and 4 as remainder.
Yes, 58 is a composite number as it has factors other than one and itself. It has factors of 2 and 29 other than 1 and 58.
The factors of 58 are 1, 2, 29 and 58.
The odd factors are 1 and 29.