Highest Common Factor of 9614, 6281, 99997 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 9614, 6281, 99997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9614, 6281, 99997 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 9614, 6281, 99997 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 9614, 6281, 99997 is 1.
HCF(9614, 6281, 99997) = 1
HCF of 9614, 6281, 99997 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9614, 6281, 99997 is 1.
Highest Common Factor of 9614,6281,99997 is 1
Step 1: Since 9614 > 6281, we apply the division lemma to 9614 and 6281, to get
9614 = 6281 x 1 + 3333
Step 2: Since the reminder 6281 ≠ 0, we apply division lemma to 3333 and 6281, to get
6281 = 3333 x 1 + 2948
Step 3: We consider the new divisor 3333 and the new remainder 2948, and apply the division lemma to get
3333 = 2948 x 1 + 385
We consider the new divisor 2948 and the new remainder 385,and apply the division lemma to get
2948 = 385 x 7 + 253
We consider the new divisor 385 and the new remainder 253,and apply the division lemma to get
385 = 253 x 1 + 132
We consider the new divisor 253 and the new remainder 132,and apply the division lemma to get
253 = 132 x 1 + 121
We consider the new divisor 132 and the new remainder 121,and apply the division lemma to get
132 = 121 x 1 + 11
We consider the new divisor 121 and the new remainder 11,and apply the division lemma to get
121 = 11 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 9614 and 6281 is 11
Notice that 11 = HCF(121,11) = HCF(132,121) = HCF(253,132) = HCF(385,253) = HCF(2948,385) = HCF(3333,2948) = HCF(6281,3333) = HCF(9614,6281) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 99997 > 11, we apply the division lemma to 99997 and 11, to get
99997 = 11 x 9090 + 7
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 7 and 11, to get
11 = 7 x 1 + 4
Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 99997 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(99997,11) .
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Frequently Asked Questions on HCF of 9614, 6281, 99997 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 9614, 6281, 99997?
Answer: HCF of 9614, 6281, 99997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9614, 6281, 99997 using Euclid's Algorithm?
Answer: For arbitrary numbers 9614, 6281, 99997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.