Highest Common Factor of 274, 820, 971 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, 820, 971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 820, 971 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, 820, 971 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, 820, 971 is 1.
HCF(274, 820, 971) = 1
HCF of 274, 820, 971 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, 820, 971 is 1.
Highest Common Factor of 274,820,971 is 1
Step 1: Since 820 > 274, we apply the division lemma to 820 and 274, to get
820 = 274 x 2 + 272
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 272 and 274, to get
274 = 272 x 1 + 2
Step 3: We consider the new divisor 272 and the new remainder 2, and apply the division lemma to get
272 = 2 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 274 and 820 is 2
Notice that 2 = HCF(272,2) = HCF(274,272) = HCF(820,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 971 > 2, we apply the division lemma to 971 and 2, to get
971 = 2 x 485 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 971 is 1
Notice that 1 = HCF(2,1) = HCF(971,2) .
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Frequently Asked Questions on HCF of 274, 820, 971 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, 820, 971?
Answer: HCF of 274, 820, 971 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 820, 971 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 820, 971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.