LCM

Two Numbers Three Numbers Multiple Numbers Prime Factorization Division Listing Multiples Ladder Exponents Venn Diagram Factor Tree

HCF

Two Numbers Three Numbers Multiple Numbers Prime Factorization Listing Ladder Exponents Venn Diagram Division Factor Tree All Factors By Division All Factors By Multiplication

HCF of Multiple Numbers By Prime Factorization Using Factor Tree

Multiple Numbers Two Numbers Three Numbers

Method

Prime Factorization Listing Ladder Exponents Division

Factors

Factor Tree Division Ladder

Enter Numbers (Comma Separated)
		Steps
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Answer: HCF of 18, 24, 54, 60 is 6

Step A: Find the Factors Using Factor Tree

Factor Methods

Factors of 18

		18
	↙		↘
2				9
			↙		↘
		3				3

Factors of 24

		24
	↙		↘
2				12
			↙		↘
		2				6
					↙		↘
				2				3

Factors of 54

		54
	↙		↘
2				27
			↙		↘
		3				9
					↙		↘
				3				3

Factors of 60

		60
	↙		↘
2				30
			↙		↘
		2				15
					↙		↘
				3				5

Factor Tree Help

1. Always begin with smallest prime.
2. This is the left child of given node.
3. Divide the number by that prime
4. Quotient is the right child of that node.
5. Repeat until right becomes prime factor.
6. Keep tree structure organized.

What is Factor Tree?

The factor tree method is a visual approach used to find the prime factorization of a composite number. It involves breaking down a number into its prime factors by repeatedly dividing it into smaller prime factors until only prime numbers remain which is represent in tree structure.

Step B: Find the HCF Using Prime Factorization

HCF Method

Calculate HCF

18 =	2 × 3 × 3
24 =	2 × 2 × 2 × 3
54 =	2 × 3 × 3 × 3
60 =	2 × 2 × 3 × 5

HCF

Prime Factorization Help

1. List the prime factors of numbers
2. Select common prime factors.
3. Multiply selected prime factors.
4. This gives the HCF.

What is Prime Factorization?

The prime factorization method is an effective approach to find the highest common factor or HCF of two or more numbers. The HCF represents the largest number that divides each given number without leaving any remainder.

Solved Examples

Examples

Example 1: Find the HCF of 9 and 15.
Solution:
Prime factorization of 9: 9 = 3, 3
Prime factorization of 15: 15 = 3, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(9, 15) = 3. Example 2: Find the HCF of 16 and 24.
Solution:
Prime factorization of 16: 16 = 2, 2, 2, 2
Prime factorization of 24: 24 = 2, 2, 2, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(16, 24) = 8. Example 3: Find the HCF of 12 and 18.
Solution:
Prime factorization of 12: 12 = 2, 2, 3
Prime factorization of 18: 18 = 2, 3, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(12, 18) = 6.

Exercise

1. HCF(14,21) = 7
2. HCF(21,28,35,42) = 7
3. HCF(12,16,20) = 4
4. HCF(10,15) = 5
5. HCF(12,16) = 4
6. HCF(6,9,15,18) = 3
7. HCF(14,21,28,35) = 7
8. HCF(20,25,30) = 5
9. HCF(14,21,35) = 7
10. HCF(9,12 18) = 3

Highest Common Factor (HCF)

What is HCF?

HCF is also known as Highest Common Factor, GCF or GCD. HCF is the largest number that divides each of the given numbers without leaving a remainder.
The HCF formula can be expressed as,
HCF Formula:
HCF = (a × b)/ LCM(a,b)
where, a and b = Two terms
LCM(a, b) = Least common multiple of a and b

How to find HCF?

The Highest common factor or HCF can be found using various methods, such as: Prime Factorization Method Division Method Listing Method Ladder Method Exponents Method Venn Diagram Method

FAQ

What are the steps involved to find HCF?

1. Write down the given numbers.
2. Use factor trees to find the prime factors of each number.
3. Identify the common prime factors.
4. Multiply these factors to find the HCF.

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