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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 Three Numbers By Listing Using All Factors By Division

Three Numbers Two Numbers Multiple Numbers
Method
Listing
Prime Factorization
Venn Diagram
Ladder
Exponents
Division
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Answer: HCF of 12, 18, 24 is 6

Step A: Find the Factors Using All Factors By Division

Factor Methods
Factors of 12
12
÷
1
=
12
✅
12
÷
2
=
6
✅
12
÷
3
=
4
✅
12
÷
4
=
3
⮥
Factors of 18
18
÷
1
=
18
✅
18
÷
2
=
9
✅
18
÷
3
=
6
✅
18
÷
6
=
3
⮥
Factors of 24
24
÷
1
=
24
✅
24
÷
2
=
12
✅
24
÷
3
=
8
✅
24
÷
4
=
6
✅
24
÷
6
=
4
⮥

All Factors By Division Help

1. Begin from 1 and divide.
2. If remainder is 0.
3. Both divisor and quotient are factors.
4. Repeat for all integers.
5. Only up to square root.

What is All Factors By Division?

The division method for finding factors involves dividing the given number by each integer, starting from 1, up to the square root of the number. Factors are the divisors that yield a whole number quotient with no remainder.

Step B: Find the HCF Using Listing

HCF Method
Calculate HCF
Factors of 12:
1
2
3
4
6
12
Factors of 18:
1
2
3
6
9
18
Factors of 24:
1
2
3
4
6
8
12
24

Listing Help

1. List factors of each number.
2. Identify common factors.
3. If no common factors, HCF is 1.
4. Otherwise, select the highest one.

What is Listing?

The listing method for finding the Highest Common Factor or HCF involves listing all factors of each number, including 1 and the number itself. The biggest common factor is the HCF of the given numbers.

Solved Examples

Examples

Example 1: Find the HCF of 10, 15 and 20.
Solution:
Factors of 10 = 1, 2, 5, 10.
Factors of 15 = 1, 3, 5, 15.
Factors of 20 = 1, 2, 4, 5, 10, 20.
Take the highest common factor.
Here, 5 is the highest common factor of 10, 15 and 20.
Therefore, HCF(10, 15, 20) = 5. Example 2: Find the HCF of 16, 24 and 32.
Solution:
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 32 = 1, 2, 4, 8, 16, 32.
Take the highest common factor.
Here, 8 is the highest common factor of 16, 24 and 32.
Therefore, HCF(16, 24, 32) = 8. Example 3: Find the HCF of 10, 20 and 30.
Solution:
Factors of 10 = 1, 2, 5, 10.
Factors of 20 = 1, 2, 4, 5, 10, 20.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Take the highest common factor.
Here, 10 is the highest common factor of 10, 20 and 30.
Therefore, HCF(10, 20, 30) = 10.

Exercise

1. HCF(12,18,24) = 6
 2. HCF(8,16,24) = 8
 3. HCF(36,48,60) = 12
 4. HCF(24, 36, 48) = 12
 5. HCF(15, 21, 27) = 3
 6. HCF(18, 27, 45) = 9
 7. HCF(24, 40, 56) = 8
 8. HCF(36, 54, 72) = 19
 9. HCF(32, 48, 96) = 96
 10. HCF(24, 68, 10) = 2

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. First find all factors for each number using all factors by division.
2. Identify common factors that appear in all three numbers.
3. Select the highest factor among them.
4. Verify the HCF by dividing with numbers without leaving a remainder.
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