Highest Common Factor of 665, 915, 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 665, 915, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 915, 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 665, 915, 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 665, 915, 509 is 1.
HCF(665, 915, 509) = 1
HCF of 665, 915, 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 665, 915, 509 is 1.
Highest Common Factor of 665,915,509 is 1
Step 1: Since 915 > 665, we apply the division lemma to 915 and 665, to get
915 = 665 x 1 + 250
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 250 and 665, to get
665 = 250 x 2 + 165
Step 3: We consider the new divisor 250 and the new remainder 165, and apply the division lemma to get
250 = 165 x 1 + 85
We consider the new divisor 165 and the new remainder 85,and apply the division lemma to get
165 = 85 x 1 + 80
We consider the new divisor 85 and the new remainder 80,and apply the division lemma to get
85 = 80 x 1 + 5
We consider the new divisor 80 and the new remainder 5,and apply the division lemma to get
80 = 5 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 665 and 915 is 5
Notice that 5 = HCF(80,5) = HCF(85,80) = HCF(165,85) = HCF(250,165) = HCF(665,250) = HCF(915,665) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 509 > 5, we apply the division lemma to 509 and 5, to get
509 = 5 x 101 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 509 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(509,5) .
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Frequently Asked Questions on HCF of 665, 915, 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 665, 915, 509?
Answer: HCF of 665, 915, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 915, 509 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 915, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.