Highest Common Factor of 6705, 7383, 96348 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 6705, 7383, 96348 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6705, 7383, 96348 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 6705, 7383, 96348 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 6705, 7383, 96348 is 3.
HCF(6705, 7383, 96348) = 3
HCF of 6705, 7383, 96348 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6705, 7383, 96348 is 3.
Highest Common Factor of 6705,7383,96348 is 3
Step 1: Since 7383 > 6705, we apply the division lemma to 7383 and 6705, to get
7383 = 6705 x 1 + 678
Step 2: Since the reminder 6705 ≠ 0, we apply division lemma to 678 and 6705, to get
6705 = 678 x 9 + 603
Step 3: We consider the new divisor 678 and the new remainder 603, and apply the division lemma to get
678 = 603 x 1 + 75
We consider the new divisor 603 and the new remainder 75,and apply the division lemma to get
603 = 75 x 8 + 3
We consider the new divisor 75 and the new remainder 3,and apply the division lemma to get
75 = 3 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6705 and 7383 is 3
Notice that 3 = HCF(75,3) = HCF(603,75) = HCF(678,603) = HCF(6705,678) = HCF(7383,6705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96348 > 3, we apply the division lemma to 96348 and 3, to get
96348 = 3 x 32116 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 96348 is 3
Notice that 3 = HCF(96348,3) .
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Frequently Asked Questions on HCF of 6705, 7383, 96348 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 6705, 7383, 96348?
Answer: HCF of 6705, 7383, 96348 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6705, 7383, 96348 using Euclid's Algorithm?
Answer: For arbitrary numbers 6705, 7383, 96348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.