The HCF of 12, 45 and 75 is 3. The highest factor that divides 12, 45 and 75 evenly gives the HCF. The subject experts use simple explanations to enhance the basic knowledge of students. The factors of 12 are 1, 2, 3, 4, 6, and 12, the factors of 45 are 1, 3, 5, 9, 15, and 45, and the factors of 75 are 1, 3, 5, 15, 25, and 75. The HCF of 12, 45 and 75 can be found using the methods of prime factorisation, long division and listing common factors.
Also read: Highest common factor
What is the HCF of 12, 45 and 75?
The answer to this question is 3. Various methods used to get the HCF of 12, 45 and 75 are given in this article for a strong understanding. The HCF of 12, 45 and 75 is 3, which divides the given numbers without leaving any remainder.
How to Find HCF of 12, 45 and 75?
The methods used to get the HCF value of 12, 45 and 75 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 12, 45 and 75 by Prime Factorisation Method
The prime factorisation of 12, 45 and 75 is:
12 = 2 × 2 × 3
45 = 3 × 3 × 5
75 = 3 × 5 × 5
Common prime factors of 12, 45 and 75 = 3
Hence, HCF (12, 45, 75) = 3
HCF of 12, 45 and 75 by Long Division Method
Using the long division method, the numbers (12, 45, 75) have to be divided by their factors to get the HCF. The HCF of 12, 45 and 75 is the divisor value when the remainder is zero after repeated division.
First, let 75 be divided by 12 and again, divide 45 by the HCF 3
No further division can be done.
Hence, HCF (12, 45, 75) = 3
HCF of 12, 45 and 75 by Listing the Factors
You can calculate the HCF of 12, 45 and 75 by listing the common factors as given below:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 75: 1, 3, 5, 15, 25, 75
There are 2 common factors of 12, 45 and 75, and they are 1 and 3.
Therefore, the highest common factor of 12, 45 and 75 is 3.
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HCF of 12, 45 and 75 Solved Example
Question: If HCF = 3 and product of three numbers = 40500, find the LCM.
Solution:
Given,
HCF = 3
Product = 40500
We know that,
HCF × LCM = Product
LCM = Product/HCF
LCM = 40500/3
LCM = 13500
Hence, the LCM is 13500.
Frequently Asked Questions on HCF of 12, 45 and 75
What is the HCF of 12, 45 and 75?
How to find the HCF of 12, 45 and 75 using the long division method?
List the methods used to find HCF of 12, 45 and 75.
In 80, 3, 119, 100, 118, 89, find the HCF of 12, 45 and 75.
Write the relation between HCF and LCM of 12, 45 and 75.
The relation between HCF and LCM of 12, 45 and 75 is
HCF × LCM = 12 × 45 × 75
HCF × LCM = 40500
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