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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 Two Numbers By Exponents Using Factor Tree

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Answer: HCF of 30, 75 is 15
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Step A: Find the Factors Using Factor Tree

Factor Methods
Factors of 30
30
↙
↘
2
15
↙
↘
3
5
Factors of 75
75
↙
↘
3
25
↙
↘
5
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 Exponents

HCF Method
Calculate HCF
30
=
2
1
×
3
1
×
5
1
75
=
3
1
×
5
2

Exponents Help

1. List the prime factors.
2. Identify common prime factors.
3. Select factors with lowest power.
4. Multiply to Find HCF.

What is Exponents?

Exponents method simplifies finding the highest common factor or HCF by listing all the prime factors of each number and then selecting the lowest power of each common prime factor to obtain the HCF.

Solved Examples

Examples

Example 1: Find the HCF of 60 and 20.
Solution:
Prime factorization of 60: 60 = 2, 2, 3, 5.
Prime factorization of 20: 20 = 2, 2, 5.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(60, 20) = 20. Example 2: Find the HCF of 24 and 36.
Solution:
Prime factorization of 24: 24 = 2, 2, 2, 3.
Prime factorization of 36: 36 = 2, 2, 3, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(24, 36) = 12. Example 3: Find the HCF of 72 and 90.
Solution:
Prime factorization of 72: 72 = 2, 2, 2, 3, 3.
Prime factorization of 90: 90 = 2, 3, 3, 5.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(72, 90) = 18.

Exercise

1. HCF(36,48) = 12. 2. HCF(42,63) = 21. 3. HCF(81,108) = 27. 4. HCF(60,72) = 12. 5. HCF(16,24) = 8. 6. HCF(12,50) = 2. 7. HCF(8,100) = 4. 8. HCF(20,24) = 4. 9. HCF(27,15) = 3. 10. HCF(15,75) = 15.

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 MethodDivision MethodListing MethodLadder MethodExponents MethodVenn Diagram Method

FAQ

What are the steps involved to find HCF?
1. Enter two numbers into the calculator.
2. Utilize a factor tree for prime factorization.
3. Convert prime factors into exponent form.
4. Multiply common factors with lowest exponents.
5. Obtain the HCF effortlessly.
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