Highest Common Factor of 987, 267, 820 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 987, 267, 820 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 267, 820 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 987, 267, 820 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 987, 267, 820 is 1.
HCF(987, 267, 820) = 1
HCF of 987, 267, 820 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 987, 267, 820 is 1.
Highest Common Factor of 987,267,820 is 1
Step 1: Since 987 > 267, we apply the division lemma to 987 and 267, to get
987 = 267 x 3 + 186
Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 186 and 267, to get
267 = 186 x 1 + 81
Step 3: We consider the new divisor 186 and the new remainder 81, and apply the division lemma to get
186 = 81 x 2 + 24
We consider the new divisor 81 and the new remainder 24,and apply the division lemma to get
81 = 24 x 3 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 987 and 267 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(81,24) = HCF(186,81) = HCF(267,186) = HCF(987,267) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 820 > 3, we apply the division lemma to 820 and 3, to get
820 = 3 x 273 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 820 is 1
Notice that 1 = HCF(3,1) = HCF(820,3) .
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Frequently Asked Questions on HCF of 987, 267, 820 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 987, 267, 820?
Answer: HCF of 987, 267, 820 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 267, 820 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 267, 820 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
