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Factors of 125
125 is a perfect cube number. 125 can be expressed as a sum of two squares in two different ways, i.e. 125 = 10^{2} + 5^{2} or 11^{2}+ 2^{2}. Let us explore more about the factors of 125! In this chapter, we will learn about the factors of 125, the factors of 125 in pairs along with some interactive examples on the prime factors of 125.
 Factors of 125: 1, 5, 25, 125
 Prime Factorization of 125: 5 × 5 × 5
What Are the Factors of 125?
 Factors of 125 are the numbers which exactly divide it and give the remainder as 0.
 When you multiply any two whole numbers with each other and get 125 as the answer, you can say that both the numbers will be the factors of 125.
 1× 125 = 125 and 5 × 25 = 125; thus, the factors of 125 are 1, 5, 25, and 125.
How to Calculate the Factors of 125?
Let's begin calculating the factors of 125, starting with the whole number 1.
 Divide 125 with this number. Is the remainder 0? Yes! So, we will get: 125 ÷ 1 = 125
 The next number is 2. 125 ÷ 2 = 62, Remainder = 1
 We will not include those numbers which leave a remainder on division.
 The next whole number is 5. Now, divide 125 with this number. 125 ÷ 5 = 25, Remainder = 0
 Proceeding in a similar manner, we obtain the factors of 125 as 1, 5, 25 and 125.
Explore factors using illustrations and interactive examples
 Factors of 25: The factors of 25 are 1, 5, and 25.
 Factors of 12: The factors of 12 are 1, 2 , 3, 6, 4, and 12.
 Factors of 225: The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75 and 225.
 Factors of 75: The factors of 75 are 1, 3, 5, 15, 25, and 75.
 Factors of 81: The factors of 81 are 1, 3, 9, 27, and 81.
Factors of 125 by Prime Factorization
Prime factorization means to express a composite number as the product of its prime factors.
 We can get the prime factors using the factor tree as shown in the figure below.
 The prime factorization of 125 can also be represented using the upsidedown division method.
Let us express 125 in terms of the product of its prime factors as 5 × 5 × 5 or in the exponent form as 5^{3}. Now that we have done the prime factorization of our number, we can multiply them factors and get the other possible composite factors. Can you try and find out if all the factors are covered?
Factors of 125 in Pairs
The pair of numbers which gives 125 when multiplied are known as the factor pairs of 125. We know that 1 × 125 = 125 and 5 × 25 = 25. Therefore, the distinct factors of 125 in pairs are (1, 125) and (5, 25).
Pair factors can be either positive or negative but they cannot be a fraction or a decimal number. Hence, we can have negative factor pairs of 125 as (1, 125) and (5, 25).
Important Notes:
 When you divide a number by its factor, the quotient of the division is also a factor.
 Factors of 125 are 1, 5, 25, and 125.
 125 is the cube of 5.
Factors of 125 Solved Examples

Example 1: List the factors of 125 and factors of 150 and find the common factors between them.
Solution:
Factors are the numbers that divide exactly without leaving any remainder.
Factors of 125 are 1, 5, 25, and 125.
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Therefore, the common factors of 25 and 150 are 1, 5, and 25.

Example 2: Peter owns a bakery. His bakery is known for its delicious cakes. Peter had to arrange 125 cakes in a rack. In how many ways can he arrange them?
Solution:
To solve this problem, we need to know the factors of 125. We know that 1, 5, 25 and 125 are the factors of 125 and the factor pairs are (1,125) and (5, 25).
The first pair shows that he can have 1 rack of 125 cakes or 125 racks of 1 cake each.
The second pair shows that he can have 5 racks of 25 cakes or 25 racks of 5 cakes each.
Thus, the cakes can be arranged in these ways.
FAQs on Factors of 125
What are all the factors of 125?
The factors of 125 are 1, 5, 25, and 125.
What are the factors of 125 and 124?
The factors of 125 are 1, 5, 25, and 125.
The factors of 124 are 1, 2, 4, 31, 62, and 124.
What are the prime factors of 125?
The distinct prime factor of 125 is 5.
Which factors of 125 add up to 30?
The factors of 125 are 1, 5, 25, and 125. The factors that sum up to 30 are 5 and 25.
What are the pair factors of 125?
1x 125 = 125, 5 x 25 = 125 , 25 x 5 =125, and 125 x 1 = 125. These 4 combinations give 125. Therefore, the distinct factors of 125 in pairs are (1, 125) and (5, 25).
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