Highest Common Factor of 905, 212, 274 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 905, 212, 274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 212, 274 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 905, 212, 274 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 905, 212, 274 is 1.
HCF(905, 212, 274) = 1
HCF of 905, 212, 274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 905, 212, 274 is 1.
Highest Common Factor of 905,212,274 is 1
Step 1: Since 905 > 212, we apply the division lemma to 905 and 212, to get
905 = 212 x 4 + 57
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 57 and 212, to get
212 = 57 x 3 + 41
Step 3: We consider the new divisor 57 and the new remainder 41, and apply the division lemma to get
57 = 41 x 1 + 16
We consider the new divisor 41 and the new remainder 16,and apply the division lemma to get
41 = 16 x 2 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 905 and 212 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(41,16) = HCF(57,41) = HCF(212,57) = HCF(905,212) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 274 > 1, we apply the division lemma to 274 and 1, to get
274 = 1 x 274 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 274 is 1
Notice that 1 = HCF(274,1) .
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Frequently Asked Questions on HCF of 905, 212, 274 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 905, 212, 274?
Answer: HCF of 905, 212, 274 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 212, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 212, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.