Highest Common Factor of 821, 3991, 8167 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 821, 3991, 8167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 3991, 8167 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 821, 3991, 8167 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 821, 3991, 8167 is 1.
HCF(821, 3991, 8167) = 1
HCF of 821, 3991, 8167 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 3991, 8167 is 1.
Highest Common Factor of 821,3991,8167 is 1
Step 1: Since 3991 > 821, we apply the division lemma to 3991 and 821, to get
3991 = 821 x 4 + 707
Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 707 and 821, to get
821 = 707 x 1 + 114
Step 3: We consider the new divisor 707 and the new remainder 114, and apply the division lemma to get
707 = 114 x 6 + 23
We consider the new divisor 114 and the new remainder 23,and apply the division lemma to get
114 = 23 x 4 + 22
We consider the new divisor 23 and the new remainder 22,and apply the division lemma to get
23 = 22 x 1 + 1
We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 3991 is 1
Notice that 1 = HCF(22,1) = HCF(23,22) = HCF(114,23) = HCF(707,114) = HCF(821,707) = HCF(3991,821) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8167 > 1, we apply the division lemma to 8167 and 1, to get
8167 = 1 x 8167 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8167 is 1
Notice that 1 = HCF(8167,1) .
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Frequently Asked Questions on HCF of 821, 3991, 8167 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 821, 3991, 8167?
Answer: HCF of 821, 3991, 8167 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 3991, 8167 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 3991, 8167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.