Highest Common Factor of 973, 1640 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, 1640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 973, 1640 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, 1640 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, 1640 is 1.
HCF(973, 1640) = 1
HCF of 973, 1640 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, 1640 is 1.
Highest Common Factor of 973,1640 is 1
Step 1: Since 1640 > 973, we apply the division lemma to 1640 and 973, to get
1640 = 973 x 1 + 667
Step 2: Since the reminder 973 ≠ 0, we apply division lemma to 667 and 973, to get
973 = 667 x 1 + 306
Step 3: We consider the new divisor 667 and the new remainder 306, and apply the division lemma to get
667 = 306 x 2 + 55
We consider the new divisor 306 and the new remainder 55,and apply the division lemma to get
306 = 55 x 5 + 31
We consider the new divisor 55 and the new remainder 31,and apply the division lemma to get
55 = 31 x 1 + 24
We consider the new divisor 31 and the new remainder 24,and apply the division lemma to get
31 = 24 x 1 + 7
We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get
24 = 7 x 3 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 1640 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(31,24) = HCF(55,31) = HCF(306,55) = HCF(667,306) = HCF(973,667) = HCF(1640,973) .
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Frequently Asked Questions on HCF of 973, 1640 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, 1640?
Answer: HCF of 973, 1640 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 973, 1640 using Euclid's Algorithm?
Answer: For arbitrary numbers 973, 1640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.