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Factors of 75 Prime Factorization, Factor Tree & Division Method Explained
IMPORTANT LINKS
Factors are the numbers that divide another number exactly, leaving no remainder. In simple terms, if a number divides another number completely, it is called a factor. For example, if you divide 12 by 3, the answer is 4 with no remainder. So, 3 is a factor of 12.
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Now let’s look at the number 75. The numbers that divide 75 evenly are called its factors. These are:
1, 3, 5, 15, 25, and 75.
This means:
- 1 × 75 = 75
- 3 × 25 = 75
- 5 × 15 = 75
So, these pairs of numbers multiply to give 75, which confirms they are factors of 75. These numbers divide 75 completely, so no remainder is left. That’s what makes them factors!
In this mathematics article, we will learn about the factors of
What are the Factors of 75?
Factors of 75 are the positive integers that divide 75 exactly, leaving no remainder. In simple terms, if a number divides 75 completely without anything left over, then that number is a factor of 75.
The factors of 75 are: 1, 3, 5, 15, 25, and 75.
Let’s check this:
- 75 ÷ 1 = 75
- 75 ÷ 3 = 25
- 75 ÷ 5 = 15
- 75 ÷ 15 = 5
- 75 ÷ 25 = 3
- 75 ÷ 75 = 1
All these give exact answers with no remainder. So, these are all the positive integers that divide 75 evenly. They are also the only numbers that, when multiplied in pairs, give the product 75 (like 3 × 25, 5 × 15). That’s why they are called the factors of 75.
Therefore,
Prime Factors of 75
Prime numbers are all positive integers that can only be divided by
The process of finding the prime factors of
So, the prime factorization of
Therefore, the prime factors of
Composite Factors of 75
Composite numbers can be defined as numbers that have more than the usual two factors; 1 and itself. Numbers that are not prime are composite numbers because they are divisible by more than two numbers.
We know that the factors of
The number
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Pair Factors of 75
Pair factors of a number are the pairs of two numbers that when multiplied together give the original number.
Positive pair factors of 75 are two positive numbers that, when multiplied together, give the product 75. These pairs show how 75 can be broken into two factors. The positive pair factors of 75 are:
(1, 75), (3, 25), and (5, 15).
Each pair contains two positive integers that divide 75 exactly with no remainder.
The table below shows the factor pairs of
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Factors |
Pair Factors |
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Therefore, from the above table we see that -
Negative pair factors of 75 are two negative numbers that multiply together to give the product +75. Since the product of two negative integers is positive, these pairs are also valid factors of 75. The negative pair factors of 75 are:
(-1, -75), (-3, -25), and (-5, -15).
Each pair consists of negative integers that divide 75 exactly with no remainder.
Similarly, we can find the negative factor pairs of
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Factors |
Negative Factor Pairs |
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Therefore, from the above table we see that negative factor pairs of
Common Factors of 75
Common factors of two or more numbers are the numbers that divide both the numbers leaving zero as the remainder. Let us understand this with the help of an example.
Example: Find the common factors of
First write the factors of
Factors of
Factors of
So, the common factors of both the numbers are
Steps to find Factors of 75
Let us understand how to find the factors of
Step 1: Start by dividing
Step 2: Check each integer to see if it divides evenly into
Step 3: The only positive integers that divide evenly into
Therefore, these are the factors of
How to Find the Factors of 75?
We can find the factors of
- Prime factorization of
. - Factor tree method to find factors of
. - Division method to find factors of
.
Prime Factorisation of 75:
Prime factorization is the process of expressing a composite number as a product of its prime factors. A composite number is any positive integer greater than
To find the prime factorization of
Step 1: To find the prime factors of
Step 2: Next, we try dividing
Step 3: Again, divide
Step 4: Now, we cannot divide
Therefore, the prime factorization of
Factor Tree Method to Find Factors of 75:
The factor tree method can be a useful way to visually see the prime factors of a number and to find all of the factors. The method can also be extended to larger numbers by continuing to factor each factor until only prime numbers are left.
Here are the steps to use the factor tree method to find the factors of
Step 1: To find the factors of
Step 2: First, select the factor pair with the smallest prime number. Here, we can take it as
Step 3:
Step 4: As both the numbers in the last step are prime, i.e.
Step 5: Bringing the prime factors all together, we get
Let us see how a factor tree of
Division Method to Find Factors of 75:
The division method is a systematic way of finding all the factors of a number. To use the division method to find the factors of
Step 1: When we divide
Step 2: At the same time, when we divide
Step 3: Try to divide
Therefore, the factors of
Factors of 75 Summary
- The factors of
- The factors of
- The prime factors of
- The negative factors of
- The positive factor pairs of
- The negative factor pairs of
- The prime factorization of
- The sum of factors of
Important Notes
- Prime factors are not the same as all factors. Prime factors are only the prime numbers that multiply to give the original number.
- If a number has an odd number of factors, it means the number is a perfect square.
- Every number has at least two factors: 1 and the number itself.
- There are no whole number factors between a number n and n/2 (except for the number itself).
- A number that has more than two factors is called a composite number.
- 1 is not a prime number, and 2 is the smallest prime number.
Factors of 75 Solved Examples
Example 1: Write
Solution:
To get the prime factors of
So,
Example 2: Find the common factors of
Solution:
First write the factors of
Factors of
Factors of
So, the common factors of both the numbers are
Example 3: Write 60 as a product of prime factors.
Solution:
We start dividing 60 by the smallest prime number:
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
So, the prime factorization of 60 is: 60 = 2 × 2 × 3 × 5
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FAQs For Factors of 75
What are all factors of 75?
The factors of
What are all the prime factors of 75?
The prime factors of
How many factors are there for number 75?
The factors of
What is the product of all the prime factors of 75?
The product of all the prime factors of
What are the positive and negative pair factors of 75?
The positive factor pairs of
What is the sum of the factors of 75?
The factors of
Is 75 a composite number?
Yes, 75 is a composite number because it has more than two factors.