Highest Common Factor of 997, 6740, 6968 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, 6740, 6968 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 6740, 6968 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, 6740, 6968 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, 6740, 6968 is 1.
HCF(997, 6740, 6968) = 1
HCF of 997, 6740, 6968 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, 6740, 6968 is 1.
Highest Common Factor of 997,6740,6968 is 1
Step 1: Since 6740 > 997, we apply the division lemma to 6740 and 997, to get
6740 = 997 x 6 + 758
Step 2: Since the reminder 997 ≠ 0, we apply division lemma to 758 and 997, to get
997 = 758 x 1 + 239
Step 3: We consider the new divisor 758 and the new remainder 239, and apply the division lemma to get
758 = 239 x 3 + 41
We consider the new divisor 239 and the new remainder 41,and apply the division lemma to get
239 = 41 x 5 + 34
We consider the new divisor 41 and the new remainder 34,and apply the division lemma to get
41 = 34 x 1 + 7
We consider the new divisor 34 and the new remainder 7,and apply the division lemma to get
34 = 7 x 4 + 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 6740 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(34,7) = HCF(41,34) = HCF(239,41) = HCF(758,239) = HCF(997,758) = HCF(6740,997) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6968 > 1, we apply the division lemma to 6968 and 1, to get
6968 = 1 x 6968 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6968 is 1
Notice that 1 = HCF(6968,1) .
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Frequently Asked Questions on HCF of 997, 6740, 6968 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, 6740, 6968?
Answer: HCF of 997, 6740, 6968 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 6740, 6968 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 6740, 6968 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.