Highest Common Factor of 973, 406 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, 406 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 973, 406 is 7 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, 406 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, 406 is 7.
HCF(973, 406) = 7
HCF of 973, 406 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, 406 is 7.
Highest Common Factor of 973,406 is 7
Step 1: Since 973 > 406, we apply the division lemma to 973 and 406, to get
973 = 406 x 2 + 161
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 161 and 406, to get
406 = 161 x 2 + 84
Step 3: We consider the new divisor 161 and the new remainder 84, and apply the division lemma to get
161 = 84 x 1 + 77
We consider the new divisor 84 and the new remainder 77,and apply the division lemma to get
84 = 77 x 1 + 7
We consider the new divisor 77 and the new remainder 7,and apply the division lemma to get
77 = 7 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 973 and 406 is 7
Notice that 7 = HCF(77,7) = HCF(84,77) = HCF(161,84) = HCF(406,161) = HCF(973,406) .
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Frequently Asked Questions on HCF of 973, 406 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, 406?
Answer: HCF of 973, 406 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 973, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 973, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.