Highest Common Factor of 217, 760, 590 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 217, 760, 590 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 217, 760, 590 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 217, 760, 590 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 217, 760, 590 is 1.
HCF(217, 760, 590) = 1
HCF of 217, 760, 590 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 217, 760, 590 is 1.
Highest Common Factor of 217,760,590 is 1
Step 1: Since 760 > 217, we apply the division lemma to 760 and 217, to get
760 = 217 x 3 + 109
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 109 and 217, to get
217 = 109 x 1 + 108
Step 3: We consider the new divisor 109 and the new remainder 108, and apply the division lemma to get
109 = 108 x 1 + 1
We consider the new divisor 108 and the new remainder 1, and apply the division lemma to get
108 = 1 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 217 and 760 is 1
Notice that 1 = HCF(108,1) = HCF(109,108) = HCF(217,109) = HCF(760,217) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 590 > 1, we apply the division lemma to 590 and 1, to get
590 = 1 x 590 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 590 is 1
Notice that 1 = HCF(590,1) .
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Frequently Asked Questions on HCF of 217, 760, 590 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 217, 760, 590?
Answer: HCF of 217, 760, 590 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 217, 760, 590 using Euclid's Algorithm?
Answer: For arbitrary numbers 217, 760, 590 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.