Highest Common Factor of 274, 1989, 6181 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 274, 1989, 6181 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 1989, 6181 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 274, 1989, 6181 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 274, 1989, 6181 is 1.
HCF(274, 1989, 6181) = 1
HCF of 274, 1989, 6181 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 274, 1989, 6181 is 1.
Highest Common Factor of 274,1989,6181 is 1
Step 1: Since 1989 > 274, we apply the division lemma to 1989 and 274, to get
1989 = 274 x 7 + 71
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 71 and 274, to get
274 = 71 x 3 + 61
Step 3: We consider the new divisor 71 and the new remainder 61, and apply the division lemma to get
71 = 61 x 1 + 10
We consider the new divisor 61 and the new remainder 10,and apply the division lemma to get
61 = 10 x 6 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 274 and 1989 is 1
Notice that 1 = HCF(10,1) = HCF(61,10) = HCF(71,61) = HCF(274,71) = HCF(1989,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6181 > 1, we apply the division lemma to 6181 and 1, to get
6181 = 1 x 6181 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6181 is 1
Notice that 1 = HCF(6181,1) .
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Frequently Asked Questions on HCF of 274, 1989, 6181 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 274, 1989, 6181?
Answer: HCF of 274, 1989, 6181 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 1989, 6181 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 1989, 6181 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.