Highest Common Factor of 509, 816, 519 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 509, 816, 519 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 816, 519 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 509, 816, 519 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 509, 816, 519 is 1.
HCF(509, 816, 519) = 1
HCF of 509, 816, 519 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 509, 816, 519 is 1.
Highest Common Factor of 509,816,519 is 1
Step 1: Since 816 > 509, we apply the division lemma to 816 and 509, to get
816 = 509 x 1 + 307
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 307 and 509, to get
509 = 307 x 1 + 202
Step 3: We consider the new divisor 307 and the new remainder 202, and apply the division lemma to get
307 = 202 x 1 + 105
We consider the new divisor 202 and the new remainder 105,and apply the division lemma to get
202 = 105 x 1 + 97
We consider the new divisor 105 and the new remainder 97,and apply the division lemma to get
105 = 97 x 1 + 8
We consider the new divisor 97 and the new remainder 8,and apply the division lemma to get
97 = 8 x 12 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 509 and 816 is 1
Notice that 1 = HCF(8,1) = HCF(97,8) = HCF(105,97) = HCF(202,105) = HCF(307,202) = HCF(509,307) = HCF(816,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 519 > 1, we apply the division lemma to 519 and 1, to get
519 = 1 x 519 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 519 is 1
Notice that 1 = HCF(519,1) .
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Frequently Asked Questions on HCF of 509, 816, 519 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 509, 816, 519?
Answer: HCF of 509, 816, 519 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 816, 519 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 816, 519 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.