Highest Common Factor of 905, 2159 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 905, 2159 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 2159 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 905, 2159 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 905, 2159 is 1.
HCF(905, 2159) = 1
HCF of 905, 2159 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 905, 2159 is 1.
Highest Common Factor of 905,2159 is 1
Step 1: Since 2159 > 905, we apply the division lemma to 2159 and 905, to get
2159 = 905 x 2 + 349
Step 2: Since the reminder 905 ≠ 0, we apply division lemma to 349 and 905, to get
905 = 349 x 2 + 207
Step 3: We consider the new divisor 349 and the new remainder 207, and apply the division lemma to get
349 = 207 x 1 + 142
We consider the new divisor 207 and the new remainder 142,and apply the division lemma to get
207 = 142 x 1 + 65
We consider the new divisor 142 and the new remainder 65,and apply the division lemma to get
142 = 65 x 2 + 12
We consider the new divisor 65 and the new remainder 12,and apply the division lemma to get
65 = 12 x 5 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 905 and 2159 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(65,12) = HCF(142,65) = HCF(207,142) = HCF(349,207) = HCF(905,349) = HCF(2159,905) .
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Frequently Asked Questions on HCF of 905, 2159 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 905, 2159?
Answer: HCF of 905, 2159 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 2159 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 2159 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.