Highest Common Factor of 410, 697, 851 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 410, 697, 851 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 410, 697, 851 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 410, 697, 851 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 410, 697, 851 is 1.
HCF(410, 697, 851) = 1
HCF of 410, 697, 851 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 410, 697, 851 is 1.
Highest Common Factor of 410,697,851 is 1
Step 1: Since 697 > 410, we apply the division lemma to 697 and 410, to get
697 = 410 x 1 + 287
Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 287 and 410, to get
410 = 287 x 1 + 123
Step 3: We consider the new divisor 287 and the new remainder 123, and apply the division lemma to get
287 = 123 x 2 + 41
We consider the new divisor 123 and the new remainder 41, and apply the division lemma to get
123 = 41 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 41, the HCF of 410 and 697 is 41
Notice that 41 = HCF(123,41) = HCF(287,123) = HCF(410,287) = HCF(697,410) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 851 > 41, we apply the division lemma to 851 and 41, to get
851 = 41 x 20 + 31
Step 2: Since the reminder 41 ≠ 0, we apply division lemma to 31 and 41, to get
41 = 31 x 1 + 10
Step 3: We consider the new divisor 31 and the new remainder 10, and apply the division lemma to get
31 = 10 x 3 + 1
We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 41 and 851 is 1
Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(41,31) = HCF(851,41) .
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Frequently Asked Questions on HCF of 410, 697, 851 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 410, 697, 851?
Answer: HCF of 410, 697, 851 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 410, 697, 851 using Euclid's Algorithm?
Answer: For arbitrary numbers 410, 697, 851 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.