Factors of 125 Using Prime Factorization
What are the Factors of 125?
If the number 125 is divided by a natural number such that the remainder is zero, the natural number is known as a factor of 125. Here, the quotient obtained on division is also a factor of 125.
The factors of 125 are 1, 5, 25, and 125 because all these numbers divide the number 125 evenly.
A List of the factors of 125
Divisibility rules and division facts can be used to determine the factors of 125.
Divisor | Is the number a factor of 125? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 125 = 125 |
2 | No, 125 is not even | - |
3 | No, 1 + 2 + 5 = 8 is not divisible by 3 | - |
4 | No, as 12 \(\div\) 54 = 31 and the remainder = 1 | - |
5 | Yes, ones digit of 125 is 5 | 5 x 25 = 125 |
6 | No, 125 is not even | - |
7 | No, as 125 \(\div\) 7 = 17 and the remainder = 6 | - |
8 | No, as 125 \(\div\) 8 = 15 and the remainder = 5 | - |
9 | No, as 125 \(\div\) 9 = 13 and the remainder = 8 | - |
If we continue the same way, we will notice that the factors will repeat on reaching 25.
Hence, we can stop checking the factors after 25 as they begin to repeat.
So, the factors of 125 are 1, 5, 25, and 125.
[Note: If we divide 125 by 15, we get 8 and 5 as the quotient and the remainder, respectively. So, 15 is not a factor of 125. Similarly, you can check for other numbers as well.]
The Prime Factorization of 125
If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that natural number. The process of writing this multiplication of prime factors is known as prime factorization.
The prime factorization of 125 can be represented by using a factor tree as shown below.
So, the prime factorization of 125 is 125 = 5 x 5 x 5 or \(5^3\), and the prime factor of 125 is 5.
Factor Pairs of 125
A factor pair of a number is a set of any two of its factors such that their product is the number itself. A factor pair can be negative or positive.
The positive factor pairs of 125 are (1, 125) and (5, 25).
1 x 125 = 125
5 x 25 = 125
Read More:
Positive Factor Pairs of 125
Positive Factors of 125 | Positive Factor Pairs of 125 |
|---|---|
1 x 125 | (1, 125) |
5 x 25 | (5, 25) |
Rapid Recall
The factors of 125 are 1, 5, 25 and 125.
Solved Factors of 125 Examples
Example 1: Find the common factors of 120 and 125.
Solution:
The factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
The factors of 125 = 1, 5, 25 and 125.
Therefore, the common factors of 120 and 125 are 1 and 5.
Example 2: Find the greatest common factor of 50 and 125.
Solution:
The factors of 50 = 1, 2, 5, 10, 25 and 50.
The factors of 125 = 1, 5, 25 and 125.
So, the common factors of 50 and 125 are 1, 5 and 25.
Therefore, the greatest common factor of 50 and 125 is 25.
Example 3: Annie was studying geometrical shapes and came across a rectangle with an area of 125 square centimeters. What are the possible dimensions of the rectangle?
Solution:
The area of the rectangle is 125 \(cm^2\).
Area of rectangle = length x width
125 = length x width
So, the dimensions of the rectangle will be the factor pairs of 125, which are, (1, 125), (5, 25), (25, 5) and (125, 1)
Therefore, the possible dimensions of the rectangle are:
Length in centimeters | Width in centimeters |
|---|---|
1 | 125 |
5 | 25 |
25 | 5 |
125 | 1 |
The factors of 125 are the numbers that divide 125 exactly, leaving the remainder as zero. The number 125 is exactly divisible by 1, 5, 25 and 125 only. So, the factors of 125 are 1, 5, 25 and 125.
Composite numbers are those numbers that have more than two factors.
The division of any positive number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all positive numbers.
Yes, 5 is a factor of 125 because when we divide 125 by 5, we get 25 as the quotient and 0 as the remainder.
The factors of 125 = 1, 5, 25 and 125.
Sum of the factors of 125 = 1 + 5 + 25 + 125
= 156