HCF of 36 and 84

HCF of 36 and 84 is 12. HCF or Highest Common Factor is the greatest number that divides two or more numbers. HCF is also known as Greatest Common Measure (GCM) or Greatest Common Divisor (GCD).

In this article, we will learn about how to find HCF of 36 and 84, what is HCF, finding HCF by prime factorization method, listing common factor and by long division method, HCF vs LCM of 36 and 84 along with some solved examples, and practice problems.

What is HCF?

HCF or Highest Common Factor is the greatest factor that divides the given numbers evenly. HCF can be evaluated for two or more than two numbers. It is the greatest divisor for the given numbers, which can equally or completely divide them.

In simple words, the HCF (Highest Common Factor) of two or more natural numbers is the largest possible number that divides all the given numbers.

Let us understand this HCF definition using two numbers, 9 and 18. The common factors of 9 and 18 are 1, 9, and 18. Among these numbers, 18 is the highest (largest) number. So, the HCF of 9 and 18 is 18. This is written as: HCF (9, 18) = 18.

What is HCF of 36 and 84?

Answer: The HCF of 36 and 84 is 12.

HCF of two numbers is the highest number that divides both the numbers without leaving any remainder. Thus, 12 is the highest number that can divide both 36 and 84 without leaving any remainder.

HCF of 36 and 84 Calculator

Use the below given calculator to find HCF of 36 and 84.

How to Find HCF of 36 and 84

Below are some of the methods of finding HCF of 36 and 84 by:

• By Prime Factorization Method
• By Listing Common Factors
• By Long Division Method

HCF of 36 and 84 by Prime Factorization Method

Follow the below-given steps to find the HCF of 36 and 84 using the prime factorization method.

• Find all the prime factors of 36 and 84 by the prime factorization method.
• Now write the common factors of the two numbers.
• Multiply all the common factors to get the HCF of 36 and 84.

Prime factor of 36 and 84, respectively, are,

36 = 2 × 2 × 3 × 3

84 = 2 × 2 × 3 × 7

Common prime factors of 36 and 84 are: 2, 2, 3

Hence, HCF(36, 84) = 2 × 2 × 3 = 12

Read More About, Prime Factorization

HCF of 36 and 84 by Listing Common Factor

Listing Common Factor means to find the common factors of the given numbers by listing all there factors. To began start by listing all the factors of 36 and 84 and then find all the common factors of them:

Step 1: List all the factors of 36 and 84

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Step 2: Find all the common factors of 36 and 84

Common factors of 36 and 84 are: 1, 2, 3, 4, 6, and 12.

Now, the greatest common factor of 36 and 84 is 12.

Therefore, HCF (36, 84) = 12

HCF of 36 and 84 by Long Division

Below are the steps for finding HCF of 36 and 84 by Long Division method:

• Step 1: Take 36 as the divisor and 84 as a dividend.
• Step 2: Perform division. We will get 12 as the remainder.
• Step 3: Take 12 as the new divisor and the previous divisor(36) as the new dividend.
• Step 4: Perform steps 2 and step 3 until you get the remainder as 0.

Below is the illustration of the HCF of 36 and 84 by long division method:

HCF vs LCM of 36 and 84

Highest Common Factor of 36 and 84 is 12 and Least Common Multiple of 36 and 84 is 252. LCM is the smallest common multiple of the given number where as HCF is the greatest common factor of the given number.

The LCM and HCF of 36 and 84 can be calculated as follow:

36 = 2 × 2 × 3 × 3

84 = 2 × 2 × 3 × 7

LCM (36, 84) = 2 × 2 × 3 × 3 × 7 = 252

HCF(36, 84) = 2 × 2 × 3 = 12

Note: LCM × HCF = Product of Two Numbers

Learn More About,

• HCF and LCM
• LCM Formula

Solved Example on HCF of 36 and 84

Example 1: What is the HCF of 36 and 84 if their LCM is 252?

Solution:

We know, LCM × HCF = product of numbers

HCF = Product of two numbers/LCM

HCF = 36 × 84/252

HCF = 3024/252

Therefore, the HCF(36, 84) is 12.

Example 2: Find the highest number that divides 36 and 18 exactly.

Solution:

Prime factor of 36 and 18, respectively, are,

36 = 2 × 2 × 3 × 3

18 = 2 × 3 × 3

Common prime factors of 36 and 18 are: 2, 3, 3

Hence, HCF(36,18) = 2 × 3 × 3= 18

Example 3: For two numbers, HCF = 20 and LCM = 250. If one number is 25, find the other number.

Solution:

Let the other number be x

We know, LCM × HCF = product of numbers

Hence,

20 × 250 = 25 × x

⇒ x = (20 × 250)/25

⇒ x = (5000)/25

⇒ x = 200

Practice Problems

Some of the practice problems on HCF are given below:

Problem 1: Find HCF of 92 and 152.

Problem 2: Find LCM and HCF of 30 and 96.

Problem 3: GCD and LCM of two numbers are 15 and 100 respectively. If one number is 30, find the other number.

Problem 4:. The product of two numbers is 138. If their HCF is 6, what is their LCM?

Practice More,

• Problems on HCF and LCM
• LCM and HCF MCQs

HCF of 36 and 84: FAQs

What is HCF of 36 and 84?

The HCF of 36 and 84 is 12.

What are Methods Used to Find HCF of 36 and 84?

The methods used to find the LCM of 36 and 84 are:

• Prime Factorization Method
• Long Division Method
• Listing Common Factors

What are the GCF and LCM of 36 and 84 respectively?

Highest Common Factor of 36 and 84 is 12 and Least Common Factor of 36 and 84 is 252.

If HCF of 84 and 36 is 12, Find its LCM.

We know, LCM × HCF = product of numbers

LCM = Product of two numbers/HCF

LCM = 36 × 84/12

LCM(36, 84) = 252