Highest Common Factor of 639, 31776 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 639, 31776 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 639, 31776 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 639, 31776 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 639, 31776 is 3.
HCF(639, 31776) = 3
HCF of 639, 31776 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 639, 31776 is 3.
Highest Common Factor of 639,31776 is 3
Step 1: Since 31776 > 639, we apply the division lemma to 31776 and 639, to get
31776 = 639 x 49 + 465
Step 2: Since the reminder 639 ≠ 0, we apply division lemma to 465 and 639, to get
639 = 465 x 1 + 174
Step 3: We consider the new divisor 465 and the new remainder 174, and apply the division lemma to get
465 = 174 x 2 + 117
We consider the new divisor 174 and the new remainder 117,and apply the division lemma to get
174 = 117 x 1 + 57
We consider the new divisor 117 and the new remainder 57,and apply the division lemma to get
117 = 57 x 2 + 3
We consider the new divisor 57 and the new remainder 3,and apply the division lemma to get
57 = 3 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 639 and 31776 is 3
Notice that 3 = HCF(57,3) = HCF(117,57) = HCF(174,117) = HCF(465,174) = HCF(639,465) = HCF(31776,639) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 639, 31776 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 639, 31776?
Answer: HCF of 639, 31776 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 639, 31776 using Euclid's Algorithm?
Answer: For arbitrary numbers 639, 31776 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.