Highest Common Factor of 96, 216, 639 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 96, 216, 639 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 96, 216, 639 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 96, 216, 639 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 96, 216, 639 is 3.
HCF(96, 216, 639) = 3
HCF of 96, 216, 639 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 96, 216, 639 is 3.
Highest Common Factor of 96,216,639 is 3
Step 1: Since 216 > 96, we apply the division lemma to 216 and 96, to get
216 = 96 x 2 + 24
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 24 and 96, to get
96 = 24 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 96 and 216 is 24
Notice that 24 = HCF(96,24) = HCF(216,96) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 639 > 24, we apply the division lemma to 639 and 24, to get
639 = 24 x 26 + 15
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 15 and 24, to get
24 = 15 x 1 + 9
Step 3: We consider the new divisor 15 and the new remainder 9, and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 24 and 639 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(639,24) .
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Frequently Asked Questions on HCF of 96, 216, 639 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 96, 216, 639?
Answer: HCF of 96, 216, 639 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 96, 216, 639 using Euclid's Algorithm?
Answer: For arbitrary numbers 96, 216, 639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.