Highest Common Factor of 2174, 8363 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 2174, 8363 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2174, 8363 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 2174, 8363 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 2174, 8363 is 1.
HCF(2174, 8363) = 1
HCF of 2174, 8363 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2174, 8363 is 1.
Highest Common Factor of 2174,8363 is 1
Step 1: Since 8363 > 2174, we apply the division lemma to 8363 and 2174, to get
8363 = 2174 x 3 + 1841
Step 2: Since the reminder 2174 ≠ 0, we apply division lemma to 1841 and 2174, to get
2174 = 1841 x 1 + 333
Step 3: We consider the new divisor 1841 and the new remainder 333, and apply the division lemma to get
1841 = 333 x 5 + 176
We consider the new divisor 333 and the new remainder 176,and apply the division lemma to get
333 = 176 x 1 + 157
We consider the new divisor 176 and the new remainder 157,and apply the division lemma to get
176 = 157 x 1 + 19
We consider the new divisor 157 and the new remainder 19,and apply the division lemma to get
157 = 19 x 8 + 5
We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get
19 = 5 x 3 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2174 and 8363 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(157,19) = HCF(176,157) = HCF(333,176) = HCF(1841,333) = HCF(2174,1841) = HCF(8363,2174) .
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Frequently Asked Questions on HCF of 2174, 8363 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 2174, 8363?
Answer: HCF of 2174, 8363 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2174, 8363 using Euclid's Algorithm?
Answer: For arbitrary numbers 2174, 8363 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.