Highest Common Factor of 417, 504, 565 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 417, 504, 565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 504, 565 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 417, 504, 565 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 417, 504, 565 is 1.
HCF(417, 504, 565) = 1
HCF of 417, 504, 565 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 417, 504, 565 is 1.
Highest Common Factor of 417,504,565 is 1
Step 1: Since 504 > 417, we apply the division lemma to 504 and 417, to get
504 = 417 x 1 + 87
Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 87 and 417, to get
417 = 87 x 4 + 69
Step 3: We consider the new divisor 87 and the new remainder 69, and apply the division lemma to get
87 = 69 x 1 + 18
We consider the new divisor 69 and the new remainder 18,and apply the division lemma to get
69 = 18 x 3 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 417 and 504 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(69,18) = HCF(87,69) = HCF(417,87) = HCF(504,417) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 565 > 3, we apply the division lemma to 565 and 3, to get
565 = 3 x 188 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 565 is 1
Notice that 1 = HCF(3,1) = HCF(565,3) .
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Frequently Asked Questions on HCF of 417, 504, 565 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 417, 504, 565?
Answer: HCF of 417, 504, 565 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 504, 565 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 504, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
