Highest Common Factor of 728, 663, 677 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 728, 663, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 663, 677 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 728, 663, 677 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 728, 663, 677 is 1.
HCF(728, 663, 677) = 1
HCF of 728, 663, 677 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 663, 677 is 1.
Highest Common Factor of 728,663,677 is 1
Step 1: Since 728 > 663, we apply the division lemma to 728 and 663, to get
728 = 663 x 1 + 65
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 65 and 663, to get
663 = 65 x 10 + 13
Step 3: We consider the new divisor 65 and the new remainder 13, and apply the division lemma to get
65 = 13 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 728 and 663 is 13
Notice that 13 = HCF(65,13) = HCF(663,65) = HCF(728,663) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 677 > 13, we apply the division lemma to 677 and 13, to get
677 = 13 x 52 + 1
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 1 and 13, to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 677 is 1
Notice that 1 = HCF(13,1) = HCF(677,13) .
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Frequently Asked Questions on HCF of 728, 663, 677 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 728, 663, 677?
Answer: HCF of 728, 663, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 663, 677 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 663, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
