Highest Common Factor of 1997, 8640 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 1997, 8640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1997, 8640 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 1997, 8640 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 1997, 8640 is 1.
HCF(1997, 8640) = 1
HCF of 1997, 8640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1997, 8640 is 1.
Highest Common Factor of 1997,8640 is 1
Step 1: Since 8640 > 1997, we apply the division lemma to 8640 and 1997, to get
8640 = 1997 x 4 + 652
Step 2: Since the reminder 1997 ≠ 0, we apply division lemma to 652 and 1997, to get
1997 = 652 x 3 + 41
Step 3: We consider the new divisor 652 and the new remainder 41, and apply the division lemma to get
652 = 41 x 15 + 37
We consider the new divisor 41 and the new remainder 37,and apply the division lemma to get
41 = 37 x 1 + 4
We consider the new divisor 37 and the new remainder 4,and apply the division lemma to get
37 = 4 x 9 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1997 and 8640 is 1
Notice that 1 = HCF(4,1) = HCF(37,4) = HCF(41,37) = HCF(652,41) = HCF(1997,652) = HCF(8640,1997) .
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Frequently Asked Questions on HCF of 1997, 8640 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 1997, 8640?
Answer: HCF of 1997, 8640 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1997, 8640 using Euclid's Algorithm?
Answer: For arbitrary numbers 1997, 8640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.