Highest Common Factor of 48, 72, 108 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 48, 72, 108 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 48, 72, 108 is 12 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 48, 72, 108 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 48, 72, 108 is 12.
HCF(48, 72, 108) = 12
HCF of 48, 72, 108 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 48, 72, 108 is 12.
Highest Common Factor of 48,72,108 is 12
Step 1: Since 72 > 48, we apply the division lemma to 72 and 48, to get
72 = 48 x 1 + 24
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 24 and 48, to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 48 and 72 is 24
Notice that 24 = HCF(48,24) = HCF(72,48) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 24, we apply the division lemma to 108 and 24, to get
108 = 24 x 4 + 12
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 12 and 24, to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 24 and 108 is 12
Notice that 12 = HCF(24,12) = HCF(108,24) .
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Frequently Asked Questions on HCF of 48, 72, 108 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 48, 72, 108?
Answer: HCF of 48, 72, 108 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 48, 72, 108 using Euclid's Algorithm?
Answer: For arbitrary numbers 48, 72, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.