Highest Common Factor of 72, 195, 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 72, 195, 108 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 72, 195, 108 is 3 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 72, 195, 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 72, 195, 108 is 3.
HCF(72, 195, 108) = 3
HCF of 72, 195, 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 72, 195, 108 is 3.
Highest Common Factor of 72,195,108 is 3
Step 1: Since 195 > 72, we apply the division lemma to 195 and 72, to get
195 = 72 x 2 + 51
Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 51 and 72, to get
72 = 51 x 1 + 21
Step 3: We consider the new divisor 51 and the new remainder 21, and apply the division lemma to get
51 = 21 x 2 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 72 and 195 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(72,51) = HCF(195,72) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 3, we apply the division lemma to 108 and 3, to get
108 = 3 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 108 is 3
Notice that 3 = HCF(108,3) .
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Frequently Asked Questions on HCF of 72, 195, 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 72, 195, 108?
Answer: HCF of 72, 195, 108 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 72, 195, 108 using Euclid's Algorithm?
Answer: For arbitrary numbers 72, 195, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.