Highest Common Factor of 663, 32403 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 663, 32403 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 32403 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 663, 32403 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 663, 32403 is 3.
HCF(663, 32403) = 3
HCF of 663, 32403 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 32403 is 3.
Highest Common Factor of 663,32403 is 3
Step 1: Since 32403 > 663, we apply the division lemma to 32403 and 663, to get
32403 = 663 x 48 + 579
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 579 and 663, to get
663 = 579 x 1 + 84
Step 3: We consider the new divisor 579 and the new remainder 84, and apply the division lemma to get
579 = 84 x 6 + 75
We consider the new divisor 84 and the new remainder 75,and apply the division lemma to get
84 = 75 x 1 + 9
We consider the new divisor 75 and the new remainder 9,and apply the division lemma to get
75 = 9 x 8 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 663 and 32403 is 3
Notice that 3 = HCF(9,3) = HCF(75,9) = HCF(84,75) = HCF(579,84) = HCF(663,579) = HCF(32403,663) .
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Frequently Asked Questions on HCF of 663, 32403 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 663, 32403?
Answer: HCF of 663, 32403 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 32403 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 32403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.