Highest Common Factor of 274, 661, 710, 11 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, 661, 710, 11 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 661, 710, 11 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, 661, 710, 11 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, 661, 710, 11 is 1.
HCF(274, 661, 710, 11) = 1
HCF of 274, 661, 710, 11 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, 661, 710, 11 is 1.
Highest Common Factor of 274,661,710,11 is 1
Step 1: Since 661 > 274, we apply the division lemma to 661 and 274, to get
661 = 274 x 2 + 113
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 113 and 274, to get
274 = 113 x 2 + 48
Step 3: We consider the new divisor 113 and the new remainder 48, and apply the division lemma to get
113 = 48 x 2 + 17
We consider the new divisor 48 and the new remainder 17,and apply the division lemma to get
48 = 17 x 2 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 274 and 661 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(48,17) = HCF(113,48) = HCF(274,113) = HCF(661,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 710 > 1, we apply the division lemma to 710 and 1, to get
710 = 1 x 710 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 710 is 1
Notice that 1 = HCF(710,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 11 > 1, we apply the division lemma to 11 and 1, to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11 is 1
Notice that 1 = HCF(11,1) .
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Frequently Asked Questions on HCF of 274, 661, 710, 11 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, 661, 710, 11?
Answer: HCF of 274, 661, 710, 11 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 661, 710, 11 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 661, 710, 11 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.