Highest Common Factor of 638, 860 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 638, 860 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 860 is 2 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 638, 860 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 638, 860 is 2.
HCF(638, 860) = 2
HCF of 638, 860 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 860 is 2.
Highest Common Factor of 638,860 is 2
Step 1: Since 860 > 638, we apply the division lemma to 860 and 638, to get
860 = 638 x 1 + 222
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 222 and 638, to get
638 = 222 x 2 + 194
Step 3: We consider the new divisor 222 and the new remainder 194, and apply the division lemma to get
222 = 194 x 1 + 28
We consider the new divisor 194 and the new remainder 28,and apply the division lemma to get
194 = 28 x 6 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 638 and 860 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(194,28) = HCF(222,194) = HCF(638,222) = HCF(860,638) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 638, 860 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 638, 860?
Answer: HCF of 638, 860 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 860 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.