Highest Common Factor of 821, 510 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, 510 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 510 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, 510 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, 510 is 1.
HCF(821, 510) = 1
HCF of 821, 510 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, 510 is 1.
Highest Common Factor of 821,510 is 1
Step 1: Since 821 > 510, we apply the division lemma to 821 and 510, to get
821 = 510 x 1 + 311
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 311 and 510, to get
510 = 311 x 1 + 199
Step 3: We consider the new divisor 311 and the new remainder 199, and apply the division lemma to get
311 = 199 x 1 + 112
We consider the new divisor 199 and the new remainder 112,and apply the division lemma to get
199 = 112 x 1 + 87
We consider the new divisor 112 and the new remainder 87,and apply the division lemma to get
112 = 87 x 1 + 25
We consider the new divisor 87 and the new remainder 25,and apply the division lemma to get
87 = 25 x 3 + 12
We consider the new divisor 25 and the new remainder 12,and apply the division lemma to get
25 = 12 x 2 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 510 is 1
Notice that 1 = HCF(12,1) = HCF(25,12) = HCF(87,25) = HCF(112,87) = HCF(199,112) = HCF(311,199) = HCF(510,311) = HCF(821,510) .
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Frequently Asked Questions on HCF of 821, 510 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, 510?
Answer: HCF of 821, 510 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 510 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 510 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.