Highest Common Factor of 412, 759, 585 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 412, 759, 585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 759, 585 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 412, 759, 585 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 412, 759, 585 is 1.
HCF(412, 759, 585) = 1
HCF of 412, 759, 585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 759, 585 is 1.
Highest Common Factor of 412,759,585 is 1
Step 1: Since 759 > 412, we apply the division lemma to 759 and 412, to get
759 = 412 x 1 + 347
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 347 and 412, to get
412 = 347 x 1 + 65
Step 3: We consider the new divisor 347 and the new remainder 65, and apply the division lemma to get
347 = 65 x 5 + 22
We consider the new divisor 65 and the new remainder 22,and apply the division lemma to get
65 = 22 x 2 + 21
We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get
22 = 21 x 1 + 1
We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 412 and 759 is 1
Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(65,22) = HCF(347,65) = HCF(412,347) = HCF(759,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 585 > 1, we apply the division lemma to 585 and 1, to get
585 = 1 x 585 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 585 is 1
Notice that 1 = HCF(585,1) .
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Frequently Asked Questions on HCF of 412, 759, 585 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 412, 759, 585?
Answer: HCF of 412, 759, 585 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 759, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 759, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.