Highest Common Factor of 682, 451, 871 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 682, 451, 871 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 451, 871 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 682, 451, 871 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 682, 451, 871 is 1.
HCF(682, 451, 871) = 1
HCF of 682, 451, 871 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 682, 451, 871 is 1.
Highest Common Factor of 682,451,871 is 1
Step 1: Since 682 > 451, we apply the division lemma to 682 and 451, to get
682 = 451 x 1 + 231
Step 2: Since the reminder 451 ≠ 0, we apply division lemma to 231 and 451, to get
451 = 231 x 1 + 220
Step 3: We consider the new divisor 231 and the new remainder 220, and apply the division lemma to get
231 = 220 x 1 + 11
We consider the new divisor 220 and the new remainder 11, and apply the division lemma to get
220 = 11 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 682 and 451 is 11
Notice that 11 = HCF(220,11) = HCF(231,220) = HCF(451,231) = HCF(682,451) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 871 > 11, we apply the division lemma to 871 and 11, to get
871 = 11 x 79 + 2
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 2 and 11, to get
11 = 2 x 5 + 1
Step 3: 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 11 and 871 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(871,11) .
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Frequently Asked Questions on HCF of 682, 451, 871 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 682, 451, 871?
Answer: HCF of 682, 451, 871 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 451, 871 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 451, 871 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.