Highest Common Factor of 728, 973, 205, 655 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, 973, 205, 655 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 973, 205, 655 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, 973, 205, 655 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, 973, 205, 655 is 1.
HCF(728, 973, 205, 655) = 1
HCF of 728, 973, 205, 655 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, 973, 205, 655 is 1.
Highest Common Factor of 728,973,205,655 is 1
Step 1: Since 973 > 728, we apply the division lemma to 973 and 728, to get
973 = 728 x 1 + 245
Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 245 and 728, to get
728 = 245 x 2 + 238
Step 3: We consider the new divisor 245 and the new remainder 238, and apply the division lemma to get
245 = 238 x 1 + 7
We consider the new divisor 238 and the new remainder 7, and apply the division lemma to get
238 = 7 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 728 and 973 is 7
Notice that 7 = HCF(238,7) = HCF(245,238) = HCF(728,245) = HCF(973,728) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 205 > 7, we apply the division lemma to 205 and 7, to get
205 = 7 x 29 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 205 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(205,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 655 > 1, we apply the division lemma to 655 and 1, to get
655 = 1 x 655 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 655 is 1
Notice that 1 = HCF(655,1) .
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Frequently Asked Questions on HCF of 728, 973, 205, 655 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, 973, 205, 655?
Answer: HCF of 728, 973, 205, 655 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 973, 205, 655 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 973, 205, 655 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.