Highest Common Factor of 836, 710, 35 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 836, 710, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 836, 710, 35 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 836, 710, 35 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 836, 710, 35 is 1.
HCF(836, 710, 35) = 1
HCF of 836, 710, 35 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 836, 710, 35 is 1.
Highest Common Factor of 836,710,35 is 1
Step 1: Since 836 > 710, we apply the division lemma to 836 and 710, to get
836 = 710 x 1 + 126
Step 2: Since the reminder 710 ≠ 0, we apply division lemma to 126 and 710, to get
710 = 126 x 5 + 80
Step 3: We consider the new divisor 126 and the new remainder 80, and apply the division lemma to get
126 = 80 x 1 + 46
We consider the new divisor 80 and the new remainder 46,and apply the division lemma to get
80 = 46 x 1 + 34
We consider the new divisor 46 and the new remainder 34,and apply the division lemma to get
46 = 34 x 1 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 836 and 710 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(46,34) = HCF(80,46) = HCF(126,80) = HCF(710,126) = HCF(836,710) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35 > 2, we apply the division lemma to 35 and 2, to get
35 = 2 x 17 + 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 35 is 1
Notice that 1 = HCF(2,1) = HCF(35,2) .
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Frequently Asked Questions on HCF of 836, 710, 35 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 836, 710, 35?
Answer: HCF of 836, 710, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 836, 710, 35 using Euclid's Algorithm?
Answer: For arbitrary numbers 836, 710, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.