Highest Common Factor of 836, 8572, 2614 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, 8572, 2614 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 836, 8572, 2614 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 836, 8572, 2614 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, 8572, 2614 is 2.
HCF(836, 8572, 2614) = 2
HCF of 836, 8572, 2614 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, 8572, 2614 is 2.
Highest Common Factor of 836,8572,2614 is 2
Step 1: Since 8572 > 836, we apply the division lemma to 8572 and 836, to get
8572 = 836 x 10 + 212
Step 2: Since the reminder 836 ≠ 0, we apply division lemma to 212 and 836, to get
836 = 212 x 3 + 200
Step 3: We consider the new divisor 212 and the new remainder 200, and apply the division lemma to get
212 = 200 x 1 + 12
We consider the new divisor 200 and the new remainder 12,and apply the division lemma to get
200 = 12 x 16 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 836 and 8572 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(200,12) = HCF(212,200) = HCF(836,212) = HCF(8572,836) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2614 > 4, we apply the division lemma to 2614 and 4, to get
2614 = 4 x 653 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 2614 is 2
Notice that 2 = HCF(4,2) = HCF(2614,4) .
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Frequently Asked Questions on HCF of 836, 8572, 2614 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, 8572, 2614?
Answer: HCF of 836, 8572, 2614 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 836, 8572, 2614 using Euclid's Algorithm?
Answer: For arbitrary numbers 836, 8572, 2614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.