Highest Common Factor of 821, 321 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, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 321 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, 321 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, 321 is 1.
HCF(821, 321) = 1
HCF of 821, 321 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, 321 is 1.
Highest Common Factor of 821,321 is 1
Step 1: Since 821 > 321, we apply the division lemma to 821 and 321, to get
821 = 321 x 2 + 179
Step 2: Since the reminder 321 ≠ 0, we apply division lemma to 179 and 321, to get
321 = 179 x 1 + 142
Step 3: We consider the new divisor 179 and the new remainder 142, and apply the division lemma to get
179 = 142 x 1 + 37
We consider the new divisor 142 and the new remainder 37,and apply the division lemma to get
142 = 37 x 3 + 31
We consider the new divisor 37 and the new remainder 31,and apply the division lemma to get
37 = 31 x 1 + 6
We consider the new divisor 31 and the new remainder 6,and apply the division lemma to get
31 = 6 x 5 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 321 is 1
Notice that 1 = HCF(6,1) = HCF(31,6) = HCF(37,31) = HCF(142,37) = HCF(179,142) = HCF(321,179) = HCF(821,321) .
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Frequently Asked Questions on HCF of 821, 321 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, 321?
Answer: HCF of 821, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.