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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 Multiple Numbers By Prime Factorization Using Division

Multiple Numbers Two Numbers Three Numbers
Method
Prime Factorization Listing Ladder Exponents Division
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Answer: HCF of 18, 24, 54, 60 is 6

Step A: Find the Factors Using Division

Factor Methods
Factors of 18
2
18
18/2=9
3
9
⤶
9/3=3
3
3
⤶
3/3=1
1
⤶
Factors of 24
2
24
24/2=12
2
12
⤶
12/2=6
2
6
⤶
6/2=3
3
3
⤶
3/3=1
1
⤶
Factors of 54
2
54
54/2=27
3
27
⤶
27/3=9
3
9
⤶
9/3=3
3
3
⤶
3/3=1
1
⤶
Factors of 60
2
60
60/2=30
2
30
⤶
30/2=15
3
15
⤶
15/3=5
5
5
⤶
5/5=1
1
⤶

Division Help

1. Start with the smallest prime.
2. Divide the number by this prime.
3. Write the quotient below.
4. Repeat until the quotient is 1.
5. Confirm using multiplication.

What is Division?

The division method for finding factors begins by dividing the given number by the smallest prime factor like 2, 3,.. This process is repeated with successive primes until the quotient is 1.

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
=
2
x
3
=
6

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 4 and 6.
Solution:
Prime factorization of 4: 4 = 2, 2
Prime factorization of 6: 6 = 2, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(4, 6) = 2. Example 2: Find the HCF of 24 and 40.
Solution:
Prime factorization of 24: 24 = 2, 2, 2, 3
Prime factorization of 40: 40 = 2, 2, 2, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(24, 40) = 8. Example 3: Find the HCF of 8 and 12.
Solution:
Prime factorization of 8: 8 = 2, 2, 2
Prime factorization of 12: 12 = 2, 2, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(8, 12) = 4.

Exercise

1. HCF(75,100,125) = 25
 2. HCF(49,98,147) = 49
 3. HCF(20,35) = 5
 4. HCF(15,25,35) = 5
 5. HCF(16,24,32) = 8
 6. HCF(6,12,18) = 6
 7. HCF(25,30,40) = 5
 8. HCF(6,9,15,18) = 3
 9. HCF(15,18,24,30) = 3
 10. HCF(20,35,40,50) = 5

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