Highest Common Factor of 461, 727, 57 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 461, 727, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 461, 727, 57 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 461, 727, 57 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 461, 727, 57 is 1.
HCF(461, 727, 57) = 1
HCF of 461, 727, 57 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 461, 727, 57 is 1.
Highest Common Factor of 461,727,57 is 1
Step 1: Since 727 > 461, we apply the division lemma to 727 and 461, to get
727 = 461 x 1 + 266
Step 2: Since the reminder 461 ≠ 0, we apply division lemma to 266 and 461, to get
461 = 266 x 1 + 195
Step 3: We consider the new divisor 266 and the new remainder 195, and apply the division lemma to get
266 = 195 x 1 + 71
We consider the new divisor 195 and the new remainder 71,and apply the division lemma to get
195 = 71 x 2 + 53
We consider the new divisor 71 and the new remainder 53,and apply the division lemma to get
71 = 53 x 1 + 18
We consider the new divisor 53 and the new remainder 18,and apply the division lemma to get
53 = 18 x 2 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 461 and 727 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(53,18) = HCF(71,53) = HCF(195,71) = HCF(266,195) = HCF(461,266) = HCF(727,461) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57 > 1, we apply the division lemma to 57 and 1, to get
57 = 1 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57 is 1
Notice that 1 = HCF(57,1) .
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Frequently Asked Questions on HCF of 461, 727, 57 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 461, 727, 57?
Answer: HCF of 461, 727, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 461, 727, 57 using Euclid's Algorithm?
Answer: For arbitrary numbers 461, 727, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.