Highest Common Factor of 504, 835, 509 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 504, 835, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 835, 509 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 504, 835, 509 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 504, 835, 509 is 1.
HCF(504, 835, 509) = 1
HCF of 504, 835, 509 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 835, 509 is 1.
Highest Common Factor of 504,835,509 is 1
Step 1: Since 835 > 504, we apply the division lemma to 835 and 504, to get
835 = 504 x 1 + 331
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 331 and 504, to get
504 = 331 x 1 + 173
Step 3: We consider the new divisor 331 and the new remainder 173, and apply the division lemma to get
331 = 173 x 1 + 158
We consider the new divisor 173 and the new remainder 158,and apply the division lemma to get
173 = 158 x 1 + 15
We consider the new divisor 158 and the new remainder 15,and apply the division lemma to get
158 = 15 x 10 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 504 and 835 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(158,15) = HCF(173,158) = HCF(331,173) = HCF(504,331) = HCF(835,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 509 > 1, we apply the division lemma to 509 and 1, to get
509 = 1 x 509 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 509 is 1
Notice that 1 = HCF(509,1) .
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Frequently Asked Questions on HCF of 504, 835, 509 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 504, 835, 509?
Answer: HCF of 504, 835, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 835, 509 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 835, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.