Highest Common Factor of 997, 610, 560 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 997, 610, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 610, 560 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 997, 610, 560 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 997, 610, 560 is 1.
HCF(997, 610, 560) = 1
HCF of 997, 610, 560 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 997, 610, 560 is 1.
Highest Common Factor of 997,610,560 is 1
Step 1: Since 997 > 610, we apply the division lemma to 997 and 610, to get
997 = 610 x 1 + 387
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 387 and 610, to get
610 = 387 x 1 + 223
Step 3: We consider the new divisor 387 and the new remainder 223, and apply the division lemma to get
387 = 223 x 1 + 164
We consider the new divisor 223 and the new remainder 164,and apply the division lemma to get
223 = 164 x 1 + 59
We consider the new divisor 164 and the new remainder 59,and apply the division lemma to get
164 = 59 x 2 + 46
We consider the new divisor 59 and the new remainder 46,and apply the division lemma to get
59 = 46 x 1 + 13
We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get
46 = 13 x 3 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 997 and 610 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(59,46) = HCF(164,59) = HCF(223,164) = HCF(387,223) = HCF(610,387) = HCF(997,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 1, we apply the division lemma to 560 and 1, to get
560 = 1 x 560 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 560 is 1
Notice that 1 = HCF(560,1) .
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Frequently Asked Questions on HCF of 997, 610, 560 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 997, 610, 560?
Answer: HCF of 997, 610, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 610, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 610, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
