Highest Common Factor of 638, 746, 851 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, 746, 851 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 746, 851 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 638, 746, 851 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, 746, 851 is 1.
HCF(638, 746, 851) = 1
HCF of 638, 746, 851 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, 746, 851 is 1.
Highest Common Factor of 638,746,851 is 1
Step 1: Since 746 > 638, we apply the division lemma to 746 and 638, to get
746 = 638 x 1 + 108
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 108 and 638, to get
638 = 108 x 5 + 98
Step 3: We consider the new divisor 108 and the new remainder 98, and apply the division lemma to get
108 = 98 x 1 + 10
We consider the new divisor 98 and the new remainder 10,and apply the division lemma to get
98 = 10 x 9 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 638 and 746 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(98,10) = HCF(108,98) = HCF(638,108) = HCF(746,638) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 851 > 2, we apply the division lemma to 851 and 2, to get
851 = 2 x 425 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 851 is 1
Notice that 1 = HCF(2,1) = HCF(851,2) .
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Frequently Asked Questions on HCF of 638, 746, 851 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, 746, 851?
Answer: HCF of 638, 746, 851 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 746, 851 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 746, 851 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.