Highest Common Factor of 516, 826 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 516, 826 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 826 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 516, 826 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 516, 826 is 2.
HCF(516, 826) = 2
HCF of 516, 826 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 826 is 2.
Highest Common Factor of 516,826 is 2
Step 1: Since 826 > 516, we apply the division lemma to 826 and 516, to get
826 = 516 x 1 + 310
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 310 and 516, to get
516 = 310 x 1 + 206
Step 3: We consider the new divisor 310 and the new remainder 206, and apply the division lemma to get
310 = 206 x 1 + 104
We consider the new divisor 206 and the new remainder 104,and apply the division lemma to get
206 = 104 x 1 + 102
We consider the new divisor 104 and the new remainder 102,and apply the division lemma to get
104 = 102 x 1 + 2
We consider the new divisor 102 and the new remainder 2,and apply the division lemma to get
102 = 2 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 516 and 826 is 2
Notice that 2 = HCF(102,2) = HCF(104,102) = HCF(206,104) = HCF(310,206) = HCF(516,310) = HCF(826,516) .
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Frequently Asked Questions on HCF of 516, 826 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 516, 826?
Answer: HCF of 516, 826 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 826 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 826 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.