Highest Common Factor of 687, 8686, 1839 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 687, 8686, 1839 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 8686, 1839 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 687, 8686, 1839 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 687, 8686, 1839 is 1.
HCF(687, 8686, 1839) = 1
HCF of 687, 8686, 1839 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 8686, 1839 is 1.
Highest Common Factor of 687,8686,1839 is 1
Step 1: Since 8686 > 687, we apply the division lemma to 8686 and 687, to get
8686 = 687 x 12 + 442
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 442 and 687, to get
687 = 442 x 1 + 245
Step 3: We consider the new divisor 442 and the new remainder 245, and apply the division lemma to get
442 = 245 x 1 + 197
We consider the new divisor 245 and the new remainder 197,and apply the division lemma to get
245 = 197 x 1 + 48
We consider the new divisor 197 and the new remainder 48,and apply the division lemma to get
197 = 48 x 4 + 5
We consider the new divisor 48 and the new remainder 5,and apply the division lemma to get
48 = 5 x 9 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 687 and 8686 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(48,5) = HCF(197,48) = HCF(245,197) = HCF(442,245) = HCF(687,442) = HCF(8686,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1839 > 1, we apply the division lemma to 1839 and 1, to get
1839 = 1 x 1839 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1839 is 1
Notice that 1 = HCF(1839,1) .
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Frequently Asked Questions on HCF of 687, 8686, 1839 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 687, 8686, 1839?
Answer: HCF of 687, 8686, 1839 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 8686, 1839 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 8686, 1839 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
