Highest Common Factor of 854, 610, 411 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 854, 610, 411 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 610, 411 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 854, 610, 411 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 854, 610, 411 is 1.
HCF(854, 610, 411) = 1
HCF of 854, 610, 411 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 854, 610, 411 is 1.
Highest Common Factor of 854,610,411 is 1
Step 1: Since 854 > 610, we apply the division lemma to 854 and 610, to get
854 = 610 x 1 + 244
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 244 and 610, to get
610 = 244 x 2 + 122
Step 3: We consider the new divisor 244 and the new remainder 122, and apply the division lemma to get
244 = 122 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 122, the HCF of 854 and 610 is 122
Notice that 122 = HCF(244,122) = HCF(610,244) = HCF(854,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 411 > 122, we apply the division lemma to 411 and 122, to get
411 = 122 x 3 + 45
Step 2: Since the reminder 122 ≠ 0, we apply division lemma to 45 and 122, to get
122 = 45 x 2 + 32
Step 3: We consider the new divisor 45 and the new remainder 32, and apply the division lemma to get
45 = 32 x 1 + 13
We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get
32 = 13 x 2 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 122 and 411 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(45,32) = HCF(122,45) = HCF(411,122) .
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Frequently Asked Questions on HCF of 854, 610, 411 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 854, 610, 411?
Answer: HCF of 854, 610, 411 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 610, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 610, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
