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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 Division

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Answer: HCF of 30, 75 is 15

Step B: Find the HCF Using Division

HCF Method
Calculate HCF
3
30
75
5
30/
3
75/
3
10
25
10/
5
25/
5
2
5
HCF
=
3
x
5
=
15

Division Help

1. List all the numbers.
2. Take smallest common prime factor.
3. Place it on the left.
4. Divide each number.
5. Write quotients below.
6. Continue until no common factors.
7. Multiply factors on left for HCF.

What is Division?

The division method for finding the Highest Common Factor involves dividing the given numbers by their common factors until there are no common factors left. The HCF is then determined by multiplying these common factors.

Solved Examples

Examples

Example 1: Find the HCF of 56 and 84.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until common factor is present.
So, list of divisors = 2, 2, 7
Here, we multiply all these divisors to calculate the HCF.
Therefore, HCF(56, 84) = 28. Example 2: Find the HCF of 12 and 26.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until common factor is present.
So, list of divisors = 2
Here, we multiply all these divisors to calculate the HCF.
Therefore, HCF(12, 26) = 2. Example 3: Find the HCF of 30 and 40.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until common factor is present.
So, list of divisors = 2, 5
Here, we multiply all these divisors to calculate the HCF.
Therefore, HCF(30, 40) = 10.

Exercise

1. HCF(16,24) = 8
 2. HCF(9,12) = 3
 3. HCF(50,70) = 10
 4. HCF(35, 28) = 7
 5. HCF(21, 15) = 3
 6. HCF(96, 120) = 24
 7. HCF(27, 3) = 3
 8. HCF(40, 60) = 20
 9. HCF(14, 16) = 2
 10. HCF(48, 18) = 6

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. Start from the least common prime factor of both numbers.
2. Divide both numbers by the least common prime factor.
3. Repeat until the common factors found.
4. Multiply these common prime factors to calculate the HCF.
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