Highest Common Factor of 973, 6590 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, 6590 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 973, 6590 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, 6590 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, 6590 is 1.
HCF(973, 6590) = 1
HCF of 973, 6590 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, 6590 is 1.
Highest Common Factor of 973,6590 is 1
Step 1: Since 6590 > 973, we apply the division lemma to 6590 and 973, to get
6590 = 973 x 6 + 752
Step 2: Since the reminder 973 ≠ 0, we apply division lemma to 752 and 973, to get
973 = 752 x 1 + 221
Step 3: We consider the new divisor 752 and the new remainder 221, and apply the division lemma to get
752 = 221 x 3 + 89
We consider the new divisor 221 and the new remainder 89,and apply the division lemma to get
221 = 89 x 2 + 43
We consider the new divisor 89 and the new remainder 43,and apply the division lemma to get
89 = 43 x 2 + 3
We consider the new divisor 43 and the new remainder 3,and apply the division lemma to get
43 = 3 x 14 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 973 and 6590 is 1
Notice that 1 = HCF(3,1) = HCF(43,3) = HCF(89,43) = HCF(221,89) = HCF(752,221) = HCF(973,752) = HCF(6590,973) .
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Frequently Asked Questions on HCF of 973, 6590 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, 6590?
Answer: HCF of 973, 6590 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 973, 6590 using Euclid's Algorithm?
Answer: For arbitrary numbers 973, 6590 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.