Highest Common Factor of 609, 987, 822 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 609, 987, 822 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 609, 987, 822 is 3 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 609, 987, 822 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 609, 987, 822 is 3.
HCF(609, 987, 822) = 3
HCF of 609, 987, 822 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 609, 987, 822 is 3.
Highest Common Factor of 609,987,822 is 3
Step 1: Since 987 > 609, we apply the division lemma to 987 and 609, to get
987 = 609 x 1 + 378
Step 2: Since the reminder 609 ≠ 0, we apply division lemma to 378 and 609, to get
609 = 378 x 1 + 231
Step 3: We consider the new divisor 378 and the new remainder 231, and apply the division lemma to get
378 = 231 x 1 + 147
We consider the new divisor 231 and the new remainder 147,and apply the division lemma to get
231 = 147 x 1 + 84
We consider the new divisor 147 and the new remainder 84,and apply the division lemma to get
147 = 84 x 1 + 63
We consider the new divisor 84 and the new remainder 63,and apply the division lemma to get
84 = 63 x 1 + 21
We consider the new divisor 63 and the new remainder 21,and apply the division lemma to get
63 = 21 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 609 and 987 is 21
Notice that 21 = HCF(63,21) = HCF(84,63) = HCF(147,84) = HCF(231,147) = HCF(378,231) = HCF(609,378) = HCF(987,609) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 21, we apply the division lemma to 822 and 21, to get
822 = 21 x 39 + 3
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 3 and 21, to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 822 is 3
Notice that 3 = HCF(21,3) = HCF(822,21) .
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Frequently Asked Questions on HCF of 609, 987, 822 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 609, 987, 822?
Answer: HCF of 609, 987, 822 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 609, 987, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 609, 987, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.