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Factors of 75 are 1, 3, 5, 15, 25 and 75. A number's precise divisor is referred to as a factor. In other terms, the integer that divides a number exactly without producing a residue is said to be its factor.
- The numbers that, when multiplied in pairs, result in the number 75 are known as factors of 75.
- The numbers that entirely divide a given number, n, are its factors.
- It implies that an is the factor of n if the residual in n/a is zero.
Read More: Real Numbers
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Key Terms: Factors, Remainder, Prime Factorization, Integers, Decimals, Fractions, Whole Numbers, Prime Numbers, Division
What are the Factors?
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When two numbers are multiplied to obtain a product, these two numbers become the factors of the product received. On the other hand, when the factors are divided by the product, they are completely divisible, and the remainder is always zero.
For example: - 2 × 4 = 8
- In the above example, 2 and 4 become the factors of 8 respectively, whereas when 8 is divided by 2 or 4, it is divisible and the equation results in 0 as a remainder.
- Factors can be positive such as 2,3,4,5, or negative such as -2, -3, -4,-5.
- Numbers that are in fractions are not considered factors at all.
Read More: Factors and Multiples
Properties of Factors
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Below mentioned are a few properties of factors–
- We can find a factor through division and multiplication methods.
- All numbers except for 0 and 1 have at least two factors.
- Numbers that end with 5, all have a common factorize. 5.
- Numbers that end 0, have common factors such as 10 and 5.
- The number 2 is the factor for all the even numbers.
- Factors are either equal to or smaller than the given number.
Read More: Arithmetic operations
Factors of 75
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When two numbers are multiplied and the product obtained is 75, these two numbers become the factors of 75. The number 75 is also divisible by these numbers. Like any other number, 75 has positive and negative factors.
Pair factors of 75– When two numbers are multiplied to get the given number, then those two numbers are pair factors of that given number. For example: - 1×75= 75
- In the above example, 1 and 75 are pair factors of 75.
- Pair factors can be negative and positive. Examples of positive pair factors are:-
1 × 75 = 75
75 × 1 = 75
3 × 25 = 75
25 × 3 = 75
- Here (1,75) and (75,1) are similar, and (3,25) and (25,3) are similar.
- All of these numbers are the positive pair factors of 75.
- Similarly, examples of negative pair factors are: -
-1 × -75 = 75
-75 × -1 = 75
-3 × -25 = 75
-25 × -3 = 75
- Here, ( -1, -75) and (-75,-1) are similar whereas (-3,-25) and (-25,-3) are similar.
- All of these numbers are the negative pair factors of 75.
Read More: Decimal Expansion
Steps to Find Factors of 75
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To find factors, one can use the following method given below stepwise: –
STEP 1: - The given number is 75, and we are supposed to find factors of, so one should start by finding the smallest factor of 75 which is 3 ( except for 1).
STEP 2: - The next step is to divide 75 by 3, i.e., 75/3= 25, hence 3 and 25 are factors of 75.
STEP 3: - Further we need to divide 75 by its next smallest factor which is 5. Therefore, 75/5= 15, which means that 5 and 15 are factors of 75.
STEP4: - The last step is to include 75 itself and 1 in the list of factors.
Hence, one arrives at the conclusion that 1,3,5,15,25, and 75 are all factors of 75. This method of finding out factors is known as factorization.
Read More: Natural Numbers and Whole Numbers
What are Prime Factors?
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To understand the concept of prime factors we first need to know what are prime numbers. Prime numbers are a set of numbers that have only two factors,i.e. the number itself and 1. Examples of prime numbers include 2,3,5,7,11 and so on.
- There are in total 25 prime numbers between 1 to 100.
- Composite numbers are those that may be divided by more than two different numbers.
- Examples of composite numbers are 4,6,8,9 and so on.
- Now, when one talks about Prime factors, it refers to the factors that are only divisible by two numbers including 1 and the number itself.
- In order to find prime factors of a given number, the prime factorization method is used.
Read More: Multiplication and Division
Prime factors of 75- by Prime Factorization
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In the process of finding out factors of any number, the prime factorization method is extremely crucial. This method helps with finding the prime factors of a number and is highly used by students while calculating factors.
STEP 1:- When one needs to calculate the prime factors of 75, one should start by dividing the smallest factor of 75 which is 3 by 75 itself hence the obtained answer will be 75/3=25.
STEP 2:- The next step is to divide 25 by its smallest factor which is 5, hence 25/5=5.
STEP 3: – Further one needs to divide 5 by itself as it is a prime number. This method is carried out by drawing a table with two rows as shown below.
The conclusion of calculating factors of 75 through the prime factorization method is that 3 and 5 are the prime factors of 75. It can also be written as 3 × 5 × 5 = 75 or 3 × 52 = 75.
Read More: Divisibility Rules
What is a Divisibility Test?
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The divisibility test is one of the easiest methods to find factors. It involves adding the individual numbers of a given number in order to find the numbers it is divisible with. For example – for 75, one needs to add 7 and 5 and if the product is divisible by 3 then only the number 75 will be divisible by 3.
- 7+5=12 and 3×4=12, therefore the number 75 is divisible by 3, making 3 a factor of 75.
- To check if a number is divisible by 5 the last digit of that number should be 0 or 5, hence in the case of 75, the last digit is 5 making it divisible by 5 and 5 being a factor of 75.
Things to Remember
- The prime factors and factors of a number are not the same thing.
- Only one and the number itself divide prime numbers.
- The lowest prime number is 2, as 1 is not one.
- Composite numbers are those that include more than two elements.
- There are in total 25 prime numbers between 1 to 100.
- Division and multiplication are the operations used to calculate the factors.
- The method used to calculate prime factors is known as prime factorization.
Sample Questions
Ques: Find the common factors of 75 and 25. (2 Marks)
Ans:
- The factors of 75 are 1,3,5,15,25,75
- The factors of 25 are 1,5,25.
- Therefore, the common factors of 75 and 25 are 1,5,25.
Ques: Add all the positive factors of 50. (2 Marks)
Ans:
- Factors of 100 = 1,2,5,10,25,50.
- The sum of factors of 100 = 1+2+5+10+25+50= 93
- Hence, the answer is 93.
Ques: Find the common factors between 44 and 60. (2 Marks)
Ans:
- The factors of 44 are 1,2,4,11,22,44.
- The factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60.
- Therefore, the common factors between 44 and 60 are 1,2,4.
Ques: Ram wants to add a natural number to 20 so it becomes a factor of 75. What numbers should be added? (2 Marks)
Ans: Let’s assume that Ram adds x to 10. Hence x=20 becomes a factor of 75. The factors of 75 that are greater than 20 are 25 and 75.
Hence, x can be 5,55. Thus, Ram can add 5 and 55 to 20 so that it will become a factor of 75.
- X + 20 = 25
- X + 20 = 55
Ques: Find the smallest factor of 54 (except for 1). (2 Marks)
Ans:
- Factors of 54 = 1,2,3,4,6,9,18,27,54.
- Hence the smallest factor of 54 is 2.
Ques: Find the biggest factor of 72. (except for 72 itself). (2 Marks)
Ans:
- Factors of 72 = 1,2,3,4,6,9,12,18,24,36,72.
- Hence the biggest factor of 72 is 36.
Ques: Out of the given options which one of these is a factor of 75? (1 Mark)
(a) 25
(b) 6
(c) 5/10
(d) 2
Ans: Option a – 25 is one of the factors of 75 whereas options b and d are not factors of 75. Option c is a fraction.
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