Highest Common Factor of 826, 514 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 826, 514 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 826, 514 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 826, 514 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 826, 514 is 2.
HCF(826, 514) = 2
HCF of 826, 514 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 826, 514 is 2.
Highest Common Factor of 826,514 is 2
Step 1: Since 826 > 514, we apply the division lemma to 826 and 514, to get
826 = 514 x 1 + 312
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 312 and 514, to get
514 = 312 x 1 + 202
Step 3: We consider the new divisor 312 and the new remainder 202, and apply the division lemma to get
312 = 202 x 1 + 110
We consider the new divisor 202 and the new remainder 110,and apply the division lemma to get
202 = 110 x 1 + 92
We consider the new divisor 110 and the new remainder 92,and apply the division lemma to get
110 = 92 x 1 + 18
We consider the new divisor 92 and the new remainder 18,and apply the division lemma to get
92 = 18 x 5 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 826 and 514 is 2
Notice that 2 = HCF(18,2) = HCF(92,18) = HCF(110,92) = HCF(202,110) = HCF(312,202) = HCF(514,312) = HCF(826,514) .
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Frequently Asked Questions on HCF of 826, 514 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 826, 514?
Answer: HCF of 826, 514 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 826, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 826, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.