Highest Common Factor of 978, 591 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 978, 591 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 591 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 978, 591 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 978, 591 is 3.
HCF(978, 591) = 3
HCF of 978, 591 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 591 is 3.
Highest Common Factor of 978,591 is 3
Step 1: Since 978 > 591, we apply the division lemma to 978 and 591, to get
978 = 591 x 1 + 387
Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 387 and 591, to get
591 = 387 x 1 + 204
Step 3: We consider the new divisor 387 and the new remainder 204, and apply the division lemma to get
387 = 204 x 1 + 183
We consider the new divisor 204 and the new remainder 183,and apply the division lemma to get
204 = 183 x 1 + 21
We consider the new divisor 183 and the new remainder 21,and apply the division lemma to get
183 = 21 x 8 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 978 and 591 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(183,21) = HCF(204,183) = HCF(387,204) = HCF(591,387) = HCF(978,591) .
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Frequently Asked Questions on HCF of 978, 591 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 978, 591?
Answer: HCF of 978, 591 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 591 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.