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• Factors of 75 – Definition With Examples

Factors of 75 – Definition With Examples

Florence Khitsane

Updated on November 29, 2025

At Brighterly, we love showing how math fits together like a puzzle. In this simple search, you can discover more about how numbers are interconnected and how they depend on one another. The number 75, for example, has many factors. Three times 25 equals 75 – just one of many pairs that make it up.

The same number pattern holds for factors of -75, since it’s similar to 75, just with a minus sign. Despite changes in signs, math rules remain consistent. Let’s explore more!

What are the factors of 75?

Each number that divides 75 evenly is determined as its factor. Since 1 is always a factor, we begin by considering the smallest number first:

• 1×75=75
• 3×25=75
• 5×15=75

So, the factors of 75 in pairs are (1, 75), (3, 25), and (5, 15). Listing them out, all factors of 75 are:

1, 3, 5, 15, 25, 75.

Properties of factors of 75

The main properties of the factors of 75 are as follows:

• When you list the factors of 75, each factor is a number that divides 75 without leaving a remainder. 
• They are always paired — two numbers multiplying together to form 75.
• The smallest factor is always 1, and the biggest is the number itself. 
• Since 75 is an odd number, all its factors are odd as well.

Difference between factors of 75 and multiples of 75

It’s easy for children to confuse factors and multiples, but they’re actually opposites in a way.

• Factors for 75 are the numbers that divide it exactly — they fit into 75 with no remainder. Example: 3 is a factor because 3×25=75.
• Multiples of 75, on the other hand, are what you get when you multiply 75 by whole numbers: 75×1=75, 75×2=150, 75×3=225, and so on.

Factor pairs of 75

Factor pairs of 75 are two numbers that multiply together to make 75. Here they are:

• 1×75=75
• 3×25=75
• 5×15=75

That gives us the factor pairs for 75:

(1, 75), (3, 25), and (5, 15).

Additionally, keep in mind that these same pairs also function with negative numbers.

Understanding the process of finding factors of 75

Check each number one by one and see which ones divide 75 without leaving a remainder.

• Start with 1: 75 ÷ 1 = 75, so it’s a factor.
• Check 2: 75 is odd, so 2 won’t work.
• Try 3: 75 ÷ 3 = 25 — that fits.
• Try 4: doesn’t divide evenly.
• Try 5: 75 ÷ 5 = 15 — another factor pair.

Once a number is divided by a divisor, you can stop looking for factor pairs.

Another way is the prime factorization of 75, which breaks 75 down into its prime numbers. For 75, it’s 3 × 5 × 5, or 3 × 5². This shows the simplest prime factors of 75, multiplied together to make 75.

Writing factors of 75

Once your child knows the prime factorization of 75, finding all its factors becomes much easier. First, break 75 into primes: 75 = 3x5x5.

Now use these numbers to make factor pairs of 75:

• Use one 5 → 3×5 = 15
• Use both 5s → 5×15 = 75
• Use 1 to make the smallest pair → 1×75 = 75

When we list all the factors we made and so the numbers that multiply to 75, we get: 1, 3, 5, 15, 25, 75.

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Practice problems on finding factors of 75

1. Fill in the gaps with the right numbers:

• 3x___=753x \_\_\_ = 753x___=75

2. True or False:

Decide if each statement below is correct.

1. 25 is one of the factors 75.
2. 10 is a factor of 75.
3. 15×5=75.

3. Factor-finding challenge:

Write all the factors of 75 from smallest to largest.

Conclusion

Working with factors is more than memorizing numbers — it is also about developing your logical reasoning and problem-solving skills. Once you have mastered factor pairs and the use of prime factorization, you can start to multiply and divide 75. 

Frequently asked questions on factors of 75

What are factors of 75?

The factors of 75 are whole numbers that can be multiplied together to produce 75. 75 is evenly divisible by these numbers, leaving no remainder. Put another way, both numbers are regarded as factors of 75 when their product equals 75. 

What are all the factors of 75?

All factors of 75 are 1, 3, 5, 15, 25, and 75. These are the only whole numbers that divide 75 exactly. Each one can be matched with another number from the list to make a multiplication pair that equals 75.

What are the factor pairs of 75?

The factor pairs of 75 are (1, 75), (3, 25), and (5, 15).

Each pair shows two numbers that multiply together to make 75.

What is the prime factorization of 75?

The prime factorization of 75 is 3 × 5 × 5, or 3 × 5². This shows that 75 is made up of the prime factors 3 and 5.

Florence Khitsane

13 articles

Florence Khitsane is a dedicated math tutor for elementary and high school students with over 2 years of experience in the field. Florence is a well-rounded math tutor who combines various learning styles to cater to diverse students’ needs, encourage student participation, and improve learning outcomes. Her primary teaching style is proactive, STEM-emphasized, and focused on improving children’s critical thinking abilities.