Highest Common Factor of 635, 877, 662 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 635, 877, 662 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 635, 877, 662 is 1 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 635, 877, 662 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 635, 877, 662 is 1.
HCF(635, 877, 662) = 1
HCF of 635, 877, 662 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 635, 877, 662 is 1.
Highest Common Factor of 635,877,662 is 1
Step 1: Since 877 > 635, we apply the division lemma to 877 and 635, to get
877 = 635 x 1 + 242
Step 2: Since the reminder 635 ≠ 0, we apply division lemma to 242 and 635, to get
635 = 242 x 2 + 151
Step 3: We consider the new divisor 242 and the new remainder 151, and apply the division lemma to get
242 = 151 x 1 + 91
We consider the new divisor 151 and the new remainder 91,and apply the division lemma to get
151 = 91 x 1 + 60
We consider the new divisor 91 and the new remainder 60,and apply the division lemma to get
91 = 60 x 1 + 31
We consider the new divisor 60 and the new remainder 31,and apply the division lemma to get
60 = 31 x 1 + 29
We consider the new divisor 31 and the new remainder 29,and apply the division lemma to get
31 = 29 x 1 + 2
We consider the new divisor 29 and the new remainder 2,and apply the division lemma to get
29 = 2 x 14 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 635 and 877 is 1
Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(31,29) = HCF(60,31) = HCF(91,60) = HCF(151,91) = HCF(242,151) = HCF(635,242) = HCF(877,635) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 662 > 1, we apply the division lemma to 662 and 1, to get
662 = 1 x 662 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 662 is 1
Notice that 1 = HCF(662,1) .
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Frequently Asked Questions on HCF of 635, 877, 662 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 635, 877, 662?
Answer: HCF of 635, 877, 662 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 635, 877, 662 using Euclid's Algorithm?
Answer: For arbitrary numbers 635, 877, 662 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.