Highest Common Factor of 821, 648 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, 648 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 648 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, 648 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, 648 is 1.
HCF(821, 648) = 1
HCF of 821, 648 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, 648 is 1.
Highest Common Factor of 821,648 is 1
Step 1: Since 821 > 648, we apply the division lemma to 821 and 648, to get
821 = 648 x 1 + 173
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 173 and 648, to get
648 = 173 x 3 + 129
Step 3: We consider the new divisor 173 and the new remainder 129, and apply the division lemma to get
173 = 129 x 1 + 44
We consider the new divisor 129 and the new remainder 44,and apply the division lemma to get
129 = 44 x 2 + 41
We consider the new divisor 44 and the new remainder 41,and apply the division lemma to get
44 = 41 x 1 + 3
We consider the new divisor 41 and the new remainder 3,and apply the division lemma to get
41 = 3 x 13 + 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 821 and 648 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(41,3) = HCF(44,41) = HCF(129,44) = HCF(173,129) = HCF(648,173) = HCF(821,648) .
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Frequently Asked Questions on HCF of 821, 648 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, 648?
Answer: HCF of 821, 648 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.