Highest Common Factor of 536, 870, 871 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 536, 870, 871 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 536, 870, 871 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 536, 870, 871 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 536, 870, 871 is 1.
HCF(536, 870, 871) = 1
HCF of 536, 870, 871 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 536, 870, 871 is 1.
Highest Common Factor of 536,870,871 is 1
Step 1: Since 870 > 536, we apply the division lemma to 870 and 536, to get
870 = 536 x 1 + 334
Step 2: Since the reminder 536 ≠ 0, we apply division lemma to 334 and 536, to get
536 = 334 x 1 + 202
Step 3: We consider the new divisor 334 and the new remainder 202, and apply the division lemma to get
334 = 202 x 1 + 132
We consider the new divisor 202 and the new remainder 132,and apply the division lemma to get
202 = 132 x 1 + 70
We consider the new divisor 132 and the new remainder 70,and apply the division lemma to get
132 = 70 x 1 + 62
We consider the new divisor 70 and the new remainder 62,and apply the division lemma to get
70 = 62 x 1 + 8
We consider the new divisor 62 and the new remainder 8,and apply the division lemma to get
62 = 8 x 7 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 536 and 870 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(62,8) = HCF(70,62) = HCF(132,70) = HCF(202,132) = HCF(334,202) = HCF(536,334) = HCF(870,536) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 871 > 2, we apply the division lemma to 871 and 2, to get
871 = 2 x 435 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 871 is 1
Notice that 1 = HCF(2,1) = HCF(871,2) .
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Frequently Asked Questions on HCF of 536, 870, 871 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 536, 870, 871?
Answer: HCF of 536, 870, 871 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 536, 870, 871 using Euclid's Algorithm?
Answer: For arbitrary numbers 536, 870, 871 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.