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HCF of 10 and 12

HCF of 10 and 12 is the largest possible number that divides 10 and 12 exactly without any remainder. The factors of 10 and 12 are 1, 2, 5, 10 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the HCF of 10 and 12 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 10 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 10 and 12?

Answer: HCF of 10 and 12 is 2.

Explanation:

The HCF of two non-zero integers, x(10) and y(12), is the highest positive integer m(2) that divides both x(10) and y(12) without any remainder.

Methods to Find HCF of 10 and 12

Let's look at the different methods for finding the HCF of 10 and 12.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 10 and 12 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 12 and Y = 10

HCF(12, 10) = HCF(10, 12 mod 10) = HCF(10, 2)
HCF(10, 2) = HCF(2, 10 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 10 and 12 is 2.

HCF of 10 and 12 by Prime Factorization

Prime factorization of 10 and 12 is (2 × 5) and (2 × 2 × 3) respectively. As visible, 10 and 12 have only one common prime factor i.e. 2. Hence, the HCF of 10 and 12 is 2.

HCF of 10 and 12 by Long Division

HCF of 10 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 12 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 10 and 12.

☛ Also Check:

HCF of 10 and 12 Examples

Example 1: Find the HCF of 10 and 12, if their LCM is 60.

Solution:

∵ LCM × HCF = 10 × 12
⇒ HCF(10, 12) = (10 × 12)/60 = 2
Therefore, the highest common factor of 10 and 12 is 2.
Example 2: For two numbers, HCF = 2 and LCM = 60. If one number is 10, find the other number.

Solution:

Given: HCF (x, 10) = 2 and LCM (x, 10) = 60
∵ HCF × LCM = 10 × (x)
⇒ x = (HCF × LCM)/10
⇒ x = (2 × 60)/10
⇒ x = 12
Therefore, the other number is 12.
Example 3: The product of two numbers is 120. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 120
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 120/2
Therefore, the LCM is 60.

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FAQs on HCF of 10 and 12

What is the HCF of 10 and 12?

The HCF of 10 and 12 is 2. To calculate the HCF of 10 and 12, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the highest factor that exactly divides both 10 and 12, i.e., 2.

How to Find the HCF of 10 and 12 by Prime Factorization?

To find the HCF of 10 and 12, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 12 = 2 × 2 × 3.
⇒ Since 2 is the only common prime factor of 10 and 12. Hence, HCF (10, 12) = 2.
☛ Prime Numbers

If the HCF of 12 and 10 is 2, Find its LCM.

HCF(12, 10) × LCM(12, 10) = 12 × 10
Since the HCF of 12 and 10 = 2
⇒ 2 × LCM(12, 10) = 120
Therefore, LCM = 60
☛ Highest Common Factor Calculator

How to Find the HCF of 10 and 12 by Long Division Method?

To find the HCF of 10, 12 using long division method, 12 is divided by 10. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 10, 12?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 10 and 12, i.e. HCF × LCM = 10 × 12.

What are the Methods to Find HCF of 10 and 12?

There are three commonly used methods to find the HCF of 10 and 12.

By Long Division
By Prime Factorization
By Listing Common Factors

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