Highest Common Factor of 693, 873, 273 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 693, 873, 273 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 693, 873, 273 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 693, 873, 273 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 693, 873, 273 is 3.
HCF(693, 873, 273) = 3
HCF of 693, 873, 273 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 693, 873, 273 is 3.
Highest Common Factor of 693,873,273 is 3
Step 1: Since 873 > 693, we apply the division lemma to 873 and 693, to get
873 = 693 x 1 + 180
Step 2: Since the reminder 693 ≠ 0, we apply division lemma to 180 and 693, to get
693 = 180 x 3 + 153
Step 3: We consider the new divisor 180 and the new remainder 153, and apply the division lemma to get
180 = 153 x 1 + 27
We consider the new divisor 153 and the new remainder 27,and apply the division lemma to get
153 = 27 x 5 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 693 and 873 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(153,27) = HCF(180,153) = HCF(693,180) = HCF(873,693) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 273 > 9, we apply the division lemma to 273 and 9, to get
273 = 9 x 30 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, 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 9 and 273 is 3
Notice that 3 = HCF(9,3) = HCF(273,9) .
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Frequently Asked Questions on HCF of 693, 873, 273 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 693, 873, 273?
Answer: HCF of 693, 873, 273 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 693, 873, 273 using Euclid's Algorithm?
Answer: For arbitrary numbers 693, 873, 273 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.