Highest Common Factor of 510, 81406 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 510, 81406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 81406 is 2 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 510, 81406 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 510, 81406 is 2.
HCF(510, 81406) = 2
HCF of 510, 81406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 81406 is 2.
Highest Common Factor of 510,81406 is 2
Step 1: Since 81406 > 510, we apply the division lemma to 81406 and 510, to get
81406 = 510 x 159 + 316
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 316 and 510, to get
510 = 316 x 1 + 194
Step 3: We consider the new divisor 316 and the new remainder 194, and apply the division lemma to get
316 = 194 x 1 + 122
We consider the new divisor 194 and the new remainder 122,and apply the division lemma to get
194 = 122 x 1 + 72
We consider the new divisor 122 and the new remainder 72,and apply the division lemma to get
122 = 72 x 1 + 50
We consider the new divisor 72 and the new remainder 50,and apply the division lemma to get
72 = 50 x 1 + 22
We consider the new divisor 50 and the new remainder 22,and apply the division lemma to get
50 = 22 x 2 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 510 and 81406 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(50,22) = HCF(72,50) = HCF(122,72) = HCF(194,122) = HCF(316,194) = HCF(510,316) = HCF(81406,510) .
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Frequently Asked Questions on HCF of 510, 81406 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 510, 81406?
Answer: HCF of 510, 81406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 81406 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 81406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.