Highest Common Factor of 509, 585, 572, 77 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, 585, 572, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 509, 585, 572, 77 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, 585, 572, 77 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, 585, 572, 77 is 1.
HCF(509, 585, 572, 77) = 1
HCF of 509, 585, 572, 77 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, 585, 572, 77 is 1.
Highest Common Factor of 509,585,572,77 is 1
Step 1: Since 585 > 509, we apply the division lemma to 585 and 509, to get
585 = 509 x 1 + 76
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 76 and 509, to get
509 = 76 x 6 + 53
Step 3: We consider the new divisor 76 and the new remainder 53, and apply the division lemma to get
76 = 53 x 1 + 23
We consider the new divisor 53 and the new remainder 23,and apply the division lemma to get
53 = 23 x 2 + 7
We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get
23 = 7 x 3 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 509 and 585 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(53,23) = HCF(76,53) = HCF(509,76) = HCF(585,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 572 > 1, we apply the division lemma to 572 and 1, to get
572 = 1 x 572 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 572 is 1
Notice that 1 = HCF(572,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get
77 = 1 x 77 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1
Notice that 1 = HCF(77,1) .
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Frequently Asked Questions on HCF of 509, 585, 572, 77 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, 585, 572, 77?
Answer: HCF of 509, 585, 572, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 509, 585, 572, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 509, 585, 572, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.