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HCF
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HCF of Three Numbers By Exponents Using Division

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Answer: HCF of 12, 18, 24 is 6
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Step A: Find the Factors Using Division

Factor Methods
Factors of 12
2
12
12/2=6
2
6
⤶
6/2=3
3
3
⤶
3/3=1
1
⤶
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
⤶

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 Exponents

HCF Method
Calculate HCF
12
=
2
2
×
3
1
18
=
2
1
×
3
2
24
=
2
3
×
3
1

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 32, 48 and 54.
Solution:
Prime factorization of 32: 32 = 2, 2, 2, 2, 2.
Prime factorization of 48: 48 = 2, 2, 2, 2, 3.
Prime factorization of 54: 54 = 2, 3, 3, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(32, 48, 54) = 2. Example 2: Find the HCF of 45, 50 and 55.
Solution:
Prime factorization of 45: 45 = 3, 3, 5.
Prime factorization of 50: 50 = 2, 5, 5.
Prime factorization of 55: 55 = 5, 11.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(45, 50, 55) = 5. Example 3: Find the HCF of 12, 18 and 24.
Solution:
Prime factorization of 12: 12 = 2, 2, 3.
Prime factorization of 18: 18 = 2, 3, 3.
Prime factorization of 24: 24 = 2, 2, 2, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(12, 18, 24) = 6.

Exercise

1. HCF(12,15,18) = 3. 2. HCF(16,24,32) = 8. 3. HCF(24,40,56) = 8. 4. HCF(23, 52, 130) = 1. 5. HCF(22, 33, 55) = 11. 6. HCF(12, 16, 56) = 4. 7. HCF(8, 48, 72) = 8. 8. HCF(16, 52, 56) = 4. 9. HCF( 21, 33, 69) = 3. 10. HCF(6, 20, 72) = 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. Input your numbers into the calculator.
2. Employ the division method for factorization.
3. Convert prime factors into exponent form.
4. Multiply common factors with lowest exponents.
5. Obtain the HCF with precision.
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