HCF of 12 and 30

The HCF of 12 and 30 is 6. The highest integer which divides the two given numbers exactly indicates the HCF. The factors of 12 and 30 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 5, 6, 10, 15, 30, respectively. The HCF value of 12 and 30 found using the prime factorisation, long division and listing common factors are available in this article in a simple manner for students to understand easily.

What is the HCF of 12 and 30?

The answer to this question is 6. You will get to know how the HCF of 12 and 30 is found using certain methods by referring to this article. The HCF of 12 and 30 is 6, which divides both the numbers exactly.

Also read: Highest common factor

How to Find HCF of 12 and 30?

The methods used to find the HCF of 12 and 30 are:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 12 and 30 by Prime Factorisation Method

The prime factorisation of 12 and 30 is written as:

12 = 2 × 2 × 3

30 = 2 × 3 × 5

Common prime factors of 12 and 30 = 2, 3

Therefore, HCF (12, 30) = 2 × 3 = 6

HCF of 12 and 30 by Long Division Method

To find the HCF, the numbers (12, 30) should be divided by the prime factors. The HCF of 12 and 30 is the divisor value we obtain after repeated long division when the remainder is zero.

HCF of 12 and 30

No further division can be done.

Hence, HCF (12, 30) = 6

HCF of 12 and 30 by Listing Common Factors

The HCF of 12 and 30 by listing the common factors method is given below:

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 12 and 30, and they are 1, 2, 3 and 6.

Therefore, the highest common factor of 12 and 30 is 6.

Related Articles

Video Lesson on Properties of HCF and LCM

HCF of 12 and 30 Solved Example

Question: If the product of two numbers = 360 and HCF = 6, find the LCM.

Solution:

Given

Product of two numbers = 360

HCF = 6

HCF × LCM = Product of two numbers

6 × LCM = 360

LCM = 360/6

LCM = 60

Hence, the LCM is 60.

Frequently Asked Questions on HCF of 12 and 30

Q1

What is the HCF of 12 and 30 if the LCM is 60?

Given

LCM = 60

LCM × HCF = 12 × 30

HCF = (12 × 30)/ 60

HCF = 6

Q2

How to find the HCF of 12 and 30 using the long division method?

The HCF of 12 and 30 can be found using the long division method, by dividing 30 by 12. The divisor 6 we get when the remainder value is zero is the HCF.
Q3

What are the methods used to find HCF of 12 and 30?

The methods used to find the HCF of 12 and 30 are Long Division, Listing Common Factors and Prime Factorisation.
Q4

What is the HCF of 12 and 30?

The HCF of 12 and 30 is 6.
Q5

Show the relation between HCF and LCM of 12 and 30.

The relation between HCF and LCM of 12 and 30 is

HCF × LCM = 12 × 30

HCF × LCM = 360

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