Highest Common Factor of 786, 502 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 786, 502 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 786, 502 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 786, 502 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 786, 502 is 2.
HCF(786, 502) = 2
HCF of 786, 502 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 786, 502 is 2.
Highest Common Factor of 786,502 is 2
Step 1: Since 786 > 502, we apply the division lemma to 786 and 502, to get
786 = 502 x 1 + 284
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 284 and 502, to get
502 = 284 x 1 + 218
Step 3: We consider the new divisor 284 and the new remainder 218, and apply the division lemma to get
284 = 218 x 1 + 66
We consider the new divisor 218 and the new remainder 66,and apply the division lemma to get
218 = 66 x 3 + 20
We consider the new divisor 66 and the new remainder 20,and apply the division lemma to get
66 = 20 x 3 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 786 and 502 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(66,20) = HCF(218,66) = HCF(284,218) = HCF(502,284) = HCF(786,502) .
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Frequently Asked Questions on HCF of 786, 502 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 786, 502?
Answer: HCF of 786, 502 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 786, 502 using Euclid's Algorithm?
Answer: For arbitrary numbers 786, 502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.