Highest Common Factor of 1774, 2081 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 1774, 2081 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1774, 2081 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 1774, 2081 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 1774, 2081 is 1.
HCF(1774, 2081) = 1
HCF of 1774, 2081 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1774, 2081 is 1.
Highest Common Factor of 1774,2081 is 1
Step 1: Since 2081 > 1774, we apply the division lemma to 2081 and 1774, to get
2081 = 1774 x 1 + 307
Step 2: Since the reminder 1774 ≠ 0, we apply division lemma to 307 and 1774, to get
1774 = 307 x 5 + 239
Step 3: We consider the new divisor 307 and the new remainder 239, and apply the division lemma to get
307 = 239 x 1 + 68
We consider the new divisor 239 and the new remainder 68,and apply the division lemma to get
239 = 68 x 3 + 35
We consider the new divisor 68 and the new remainder 35,and apply the division lemma to get
68 = 35 x 1 + 33
We consider the new divisor 35 and the new remainder 33,and apply the division lemma to get
35 = 33 x 1 + 2
We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get
33 = 2 x 16 + 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 1774 and 2081 is 1
Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(35,33) = HCF(68,35) = HCF(239,68) = HCF(307,239) = HCF(1774,307) = HCF(2081,1774) .
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Frequently Asked Questions on HCF of 1774, 2081 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 1774, 2081?
Answer: HCF of 1774, 2081 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1774, 2081 using Euclid's Algorithm?
Answer: For arbitrary numbers 1774, 2081 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.