Highest Common Factor of 973, 2173 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 973, 2173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 973, 2173 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 973, 2173 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 973, 2173 is 1.
HCF(973, 2173) = 1
HCF of 973, 2173 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 973, 2173 is 1.
Highest Common Factor of 973,2173 is 1
Step 1: Since 2173 > 973, we apply the division lemma to 2173 and 973, to get
2173 = 973 x 2 + 227
Step 2: Since the reminder 973 ≠ 0, we apply division lemma to 227 and 973, to get
973 = 227 x 4 + 65
Step 3: We consider the new divisor 227 and the new remainder 65, and apply the division lemma to get
227 = 65 x 3 + 32
We consider the new divisor 65 and the new remainder 32,and apply the division lemma to get
65 = 32 x 2 + 1
We consider the new divisor 32 and the new remainder 1,and apply the division lemma to get
32 = 1 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 973 and 2173 is 1
Notice that 1 = HCF(32,1) = HCF(65,32) = HCF(227,65) = HCF(973,227) = HCF(2173,973) .
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Frequently Asked Questions on HCF of 973, 2173 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 973, 2173?
Answer: HCF of 973, 2173 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 973, 2173 using Euclid's Algorithm?
Answer: For arbitrary numbers 973, 2173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.