Factors of 50 Using Prime Factrization
Factors of 50
A factor of a number is a number that divides it evenly, leaving zero as the remainder. The factor of a number can be both positive or negative but it cannot be a decimal or fraction. We will learn about the factors of 50 in the following article, as well as the methodology for finding factors using a couple of methods such as divisibility rules and prime factorization.
Factors of 50
What are the Factors of 50?
The natural numbers that can divide a number evenly are known as the factors of that number. When 50 is divided by its factor, the remainder is zero, and the quotient is also a factor of 50.
Example: 5 is a factor of 50 because when we divide 50 by 5, it gives us the quotient as 10 and the remainder as 0. Here the quotient, 10, is also a factor of 50.
So, to check if any number is a factor of 50 or not, divide 50 by that number and verify that the remainder is zero or not.
The number 50 has a total of six factors: 1, 2, 5, 10, 25 and 50.
Factor List of 50
Factors of 50 can be obtained by applying the divisibility rules and division facts.
So the factors of 50 are 1, 2, 5, 10, 25, and 50.
Prime Factors of 50
A factor tree can be used to learn about the prime factors and prime factorization of 50.
From the factor tree we can see prime factorization of 50 is 2 × 5 × 5 = 2 × \(5^2\).
This means 2, 5 and 5 are the prime factors of 50.
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Factor Pairs of 50
The factor pairs of 50 are combinations of two factors of 50 which when multiplied together result in 50.
Example: (2, 25) is the factor pair of 50 as 2 x 25 = 50.
The factor pairs of a number can be obtained from the list of factors of that number. The factor pair can be a positive pair or a negative pair.
A list of positive factor pairs of 50 is given below :
So, the factor pairs for 50 are 1 and 50, 2 and 25, 5 and 10.
Rapid Recall
Solved Factors of 50 Examples
Example 1: Find the common factors of 60 and 50.
Solution:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 50: 1, 2, 5, 10, 25 and 50.
So, the common factors of 60 and 50 are 1, 2, 5 and 10.
Example 2: Find the total number of common factors of 50 and 210.
Solution:
The factors of 50 are 1, 2, 5, 10, 25 and 50
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
So the common factors of 50 and 210 are 1, 2, 5 and 10.
Hence, the total number of common factors of 50 and 210 is 4.
Example 3:
A school library has a collection of 50 books on the History of America. The books are to be arranged evenly on 5 shelves. How many books will be placed on each shelf?
Solution:
50 books are to be evenly arranged on 5 shelves.
To find how many books can be placed on each shelf we will divide 50 by 5, that is, \(\frac{50}{5}\)
= \(\frac{10\times5}{5}\) [(10,5) is a factor pair of 50]
= 10 [Divide both numerator and denominator by 5]
As a result, 10 books can be placed on one shelf.
No, when you divide 50 by 9 it will give 5 as a remainder, that is, 9 does not divide 50 evenly.
Numbers that divide 50 evenly, that is, leave zero as the remainder are known as factors of 50.
The factors of 50 are 1, 2, 5, 10, 25 and 50.
Hence, the sum of the all the factors of 50 is
= 1 + 2 + 5 + 10 + 25 + 50 = 93
Hence, the sum is 93.
Yes, 50 is a composite number as it has factors other than 1 and itself. It has factors 2, 5, 10, 25 other than 1 and 50.
The factors of 50 are 1, 2, 5, 10, 25 and 50.
So, the least factor of 50 is 1 and the greatest factor is 50 itself.