Highest Common Factor of 9712, 7335 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 9712, 7335 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9712, 7335 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 9712, 7335 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 9712, 7335 is 1.
HCF(9712, 7335) = 1
HCF of 9712, 7335 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9712, 7335 is 1.
Highest Common Factor of 9712,7335 is 1
Step 1: Since 9712 > 7335, we apply the division lemma to 9712 and 7335, to get
9712 = 7335 x 1 + 2377
Step 2: Since the reminder 7335 ≠ 0, we apply division lemma to 2377 and 7335, to get
7335 = 2377 x 3 + 204
Step 3: We consider the new divisor 2377 and the new remainder 204, and apply the division lemma to get
2377 = 204 x 11 + 133
We consider the new divisor 204 and the new remainder 133,and apply the division lemma to get
204 = 133 x 1 + 71
We consider the new divisor 133 and the new remainder 71,and apply the division lemma to get
133 = 71 x 1 + 62
We consider the new divisor 71 and the new remainder 62,and apply the division lemma to get
71 = 62 x 1 + 9
We consider the new divisor 62 and the new remainder 9,and apply the division lemma to get
62 = 9 x 6 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9712 and 7335 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(62,9) = HCF(71,62) = HCF(133,71) = HCF(204,133) = HCF(2377,204) = HCF(7335,2377) = HCF(9712,7335) .
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Frequently Asked Questions on HCF of 9712, 7335 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 9712, 7335?
Answer: HCF of 9712, 7335 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9712, 7335 using Euclid's Algorithm?
Answer: For arbitrary numbers 9712, 7335 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.