Highest Common Factor of 502, 810, 768 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 502, 810, 768 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 502, 810, 768 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 502, 810, 768 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 502, 810, 768 is 2.
HCF(502, 810, 768) = 2
HCF of 502, 810, 768 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 502, 810, 768 is 2.
Highest Common Factor of 502,810,768 is 2
Step 1: Since 810 > 502, we apply the division lemma to 810 and 502, to get
810 = 502 x 1 + 308
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 308 and 502, to get
502 = 308 x 1 + 194
Step 3: We consider the new divisor 308 and the new remainder 194, and apply the division lemma to get
308 = 194 x 1 + 114
We consider the new divisor 194 and the new remainder 114,and apply the division lemma to get
194 = 114 x 1 + 80
We consider the new divisor 114 and the new remainder 80,and apply the division lemma to get
114 = 80 x 1 + 34
We consider the new divisor 80 and the new remainder 34,and apply the division lemma to get
80 = 34 x 2 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 502 and 810 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(80,34) = HCF(114,80) = HCF(194,114) = HCF(308,194) = HCF(502,308) = HCF(810,502) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 768 > 2, we apply the division lemma to 768 and 2, to get
768 = 2 x 384 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 768 is 2
Notice that 2 = HCF(768,2) .
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Frequently Asked Questions on HCF of 502, 810, 768 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 502, 810, 768?
Answer: HCF of 502, 810, 768 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 502, 810, 768 using Euclid's Algorithm?
Answer: For arbitrary numbers 502, 810, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.