Highest Common Factor of 9765, 7314 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 9765, 7314 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9765, 7314 is 3 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 9765, 7314 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 9765, 7314 is 3.
HCF(9765, 7314) = 3
HCF of 9765, 7314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9765, 7314 is 3.
Highest Common Factor of 9765,7314 is 3
Step 1: Since 9765 > 7314, we apply the division lemma to 9765 and 7314, to get
9765 = 7314 x 1 + 2451
Step 2: Since the reminder 7314 ≠ 0, we apply division lemma to 2451 and 7314, to get
7314 = 2451 x 2 + 2412
Step 3: We consider the new divisor 2451 and the new remainder 2412, and apply the division lemma to get
2451 = 2412 x 1 + 39
We consider the new divisor 2412 and the new remainder 39,and apply the division lemma to get
2412 = 39 x 61 + 33
We consider the new divisor 39 and the new remainder 33,and apply the division lemma to get
39 = 33 x 1 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9765 and 7314 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(39,33) = HCF(2412,39) = HCF(2451,2412) = HCF(7314,2451) = HCF(9765,7314) .
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Frequently Asked Questions on HCF of 9765, 7314 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 9765, 7314?
Answer: HCF of 9765, 7314 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9765, 7314 using Euclid's Algorithm?
Answer: For arbitrary numbers 9765, 7314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
