Highest Common Factor of 816, 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 816, 639 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 816, 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 816, 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 816, 639 is 3.
HCF(816, 639) = 3
HCF of 816, 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 816, 639 is 3.
Highest Common Factor of 816,639 is 3
Step 1: Since 816 > 639, we apply the division lemma to 816 and 639, to get
816 = 639 x 1 + 177
Step 2: Since the reminder 639 ≠ 0, we apply division lemma to 177 and 639, to get
639 = 177 x 3 + 108
Step 3: We consider the new divisor 177 and the new remainder 108, and apply the division lemma to get
177 = 108 x 1 + 69
We consider the new divisor 108 and the new remainder 69,and apply the division lemma to get
108 = 69 x 1 + 39
We consider the new divisor 69 and the new remainder 39,and apply the division lemma to get
69 = 39 x 1 + 30
We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get
39 = 30 x 1 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 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 816 and 639 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(69,39) = HCF(108,69) = HCF(177,108) = HCF(639,177) = HCF(816,639) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 816, 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 816, 639?
Answer: HCF of 816, 639 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 816, 639 using Euclid's Algorithm?
Answer: For arbitrary numbers 816, 639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.