Highest Common Factor of 865, 2217 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 865, 2217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 865, 2217 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 865, 2217 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 865, 2217 is 1.
HCF(865, 2217) = 1
HCF of 865, 2217 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 865, 2217 is 1.
Highest Common Factor of 865,2217 is 1
Step 1: Since 2217 > 865, we apply the division lemma to 2217 and 865, to get
2217 = 865 x 2 + 487
Step 2: Since the reminder 865 ≠ 0, we apply division lemma to 487 and 865, to get
865 = 487 x 1 + 378
Step 3: We consider the new divisor 487 and the new remainder 378, and apply the division lemma to get
487 = 378 x 1 + 109
We consider the new divisor 378 and the new remainder 109,and apply the division lemma to get
378 = 109 x 3 + 51
We consider the new divisor 109 and the new remainder 51,and apply the division lemma to get
109 = 51 x 2 + 7
We consider the new divisor 51 and the new remainder 7,and apply the division lemma to get
51 = 7 x 7 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 865 and 2217 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(51,7) = HCF(109,51) = HCF(378,109) = HCF(487,378) = HCF(865,487) = HCF(2217,865) .
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Frequently Asked Questions on HCF of 865, 2217 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 865, 2217?
Answer: HCF of 865, 2217 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 865, 2217 using Euclid's Algorithm?
Answer: For arbitrary numbers 865, 2217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
