Highest Common Factor of 6480, 7473 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 6480, 7473 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6480, 7473 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 6480, 7473 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 6480, 7473 is 3.
HCF(6480, 7473) = 3
HCF of 6480, 7473 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6480, 7473 is 3.
Highest Common Factor of 6480,7473 is 3
Step 1: Since 7473 > 6480, we apply the division lemma to 7473 and 6480, to get
7473 = 6480 x 1 + 993
Step 2: Since the reminder 6480 ≠ 0, we apply division lemma to 993 and 6480, to get
6480 = 993 x 6 + 522
Step 3: We consider the new divisor 993 and the new remainder 522, and apply the division lemma to get
993 = 522 x 1 + 471
We consider the new divisor 522 and the new remainder 471,and apply the division lemma to get
522 = 471 x 1 + 51
We consider the new divisor 471 and the new remainder 51,and apply the division lemma to get
471 = 51 x 9 + 12
We consider the new divisor 51 and the new remainder 12,and apply the division lemma to get
51 = 12 x 4 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6480 and 7473 is 3
Notice that 3 = HCF(12,3) = HCF(51,12) = HCF(471,51) = HCF(522,471) = HCF(993,522) = HCF(6480,993) = HCF(7473,6480) .
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Frequently Asked Questions on HCF of 6480, 7473 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 6480, 7473?
Answer: HCF of 6480, 7473 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6480, 7473 using Euclid's Algorithm?
Answer: For arbitrary numbers 6480, 7473 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.