Highest Common Factor of 803, 510, 508 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 803, 510, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 803, 510, 508 is 1 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 803, 510, 508 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 803, 510, 508 is 1.
HCF(803, 510, 508) = 1
HCF of 803, 510, 508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 803, 510, 508 is 1.
Highest Common Factor of 803,510,508 is 1
Step 1: Since 803 > 510, we apply the division lemma to 803 and 510, to get
803 = 510 x 1 + 293
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 293 and 510, to get
510 = 293 x 1 + 217
Step 3: We consider the new divisor 293 and the new remainder 217, and apply the division lemma to get
293 = 217 x 1 + 76
We consider the new divisor 217 and the new remainder 76,and apply the division lemma to get
217 = 76 x 2 + 65
We consider the new divisor 76 and the new remainder 65,and apply the division lemma to get
76 = 65 x 1 + 11
We consider the new divisor 65 and the new remainder 11,and apply the division lemma to get
65 = 11 x 5 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 803 and 510 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(65,11) = HCF(76,65) = HCF(217,76) = HCF(293,217) = HCF(510,293) = HCF(803,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 1, we apply the division lemma to 508 and 1, to get
508 = 1 x 508 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 508 is 1
Notice that 1 = HCF(508,1) .
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Frequently Asked Questions on HCF of 803, 510, 508 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 803, 510, 508?
Answer: HCF of 803, 510, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 803, 510, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 803, 510, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.