Highest Common Factor of 871, 456, 413 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 871, 456, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 871, 456, 413 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 871, 456, 413 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 871, 456, 413 is 1.
HCF(871, 456, 413) = 1
HCF of 871, 456, 413 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 871, 456, 413 is 1.
Highest Common Factor of 871,456,413 is 1
Step 1: Since 871 > 456, we apply the division lemma to 871 and 456, to get
871 = 456 x 1 + 415
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 415 and 456, to get
456 = 415 x 1 + 41
Step 3: We consider the new divisor 415 and the new remainder 41, and apply the division lemma to get
415 = 41 x 10 + 5
We consider the new divisor 41 and the new remainder 5,and apply the division lemma to get
41 = 5 x 8 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 871 and 456 is 1
Notice that 1 = HCF(5,1) = HCF(41,5) = HCF(415,41) = HCF(456,415) = HCF(871,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get
413 = 1 x 413 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1
Notice that 1 = HCF(413,1) .
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Frequently Asked Questions on HCF of 871, 456, 413 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 871, 456, 413?
Answer: HCF of 871, 456, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 871, 456, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 871, 456, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.