Highest Common Factor of 6975, 8397 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 6975, 8397 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 6975, 8397 is 9 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 6975, 8397 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 6975, 8397 is 9.
HCF(6975, 8397) = 9
HCF of 6975, 8397 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6975, 8397 is 9.
Highest Common Factor of 6975,8397 is 9
Step 1: Since 8397 > 6975, we apply the division lemma to 8397 and 6975, to get
8397 = 6975 x 1 + 1422
Step 2: Since the reminder 6975 ≠ 0, we apply division lemma to 1422 and 6975, to get
6975 = 1422 x 4 + 1287
Step 3: We consider the new divisor 1422 and the new remainder 1287, and apply the division lemma to get
1422 = 1287 x 1 + 135
We consider the new divisor 1287 and the new remainder 135,and apply the division lemma to get
1287 = 135 x 9 + 72
We consider the new divisor 135 and the new remainder 72,and apply the division lemma to get
135 = 72 x 1 + 63
We consider the new divisor 72 and the new remainder 63,and apply the division lemma to get
72 = 63 x 1 + 9
We consider the new divisor 63 and the new remainder 9,and apply the division lemma to get
63 = 9 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 6975 and 8397 is 9
Notice that 9 = HCF(63,9) = HCF(72,63) = HCF(135,72) = HCF(1287,135) = HCF(1422,1287) = HCF(6975,1422) = HCF(8397,6975) .
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Frequently Asked Questions on HCF of 6975, 8397 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 6975, 8397?
Answer: HCF of 6975, 8397 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6975, 8397 using Euclid's Algorithm?
Answer: For arbitrary numbers 6975, 8397 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
