Highest Common Factor of 585, 855, 665 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 585, 855, 665 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 855, 665 is 5 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 585, 855, 665 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 585, 855, 665 is 5.
HCF(585, 855, 665) = 5
HCF of 585, 855, 665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 585, 855, 665 is 5.
Highest Common Factor of 585,855,665 is 5
Step 1: Since 855 > 585, we apply the division lemma to 855 and 585, to get
855 = 585 x 1 + 270
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 270 and 585, to get
585 = 270 x 2 + 45
Step 3: We consider the new divisor 270 and the new remainder 45, and apply the division lemma to get
270 = 45 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 585 and 855 is 45
Notice that 45 = HCF(270,45) = HCF(585,270) = HCF(855,585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 665 > 45, we apply the division lemma to 665 and 45, to get
665 = 45 x 14 + 35
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 35 and 45, to get
45 = 35 x 1 + 10
Step 3: We consider the new divisor 35 and the new remainder 10, and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 45 and 665 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(665,45) .
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Frequently Asked Questions on HCF of 585, 855, 665 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 585, 855, 665?
Answer: HCF of 585, 855, 665 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 855, 665 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 855, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.