Highest Common Factor of 777, 9723 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 777, 9723 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 777, 9723 is 21 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 777, 9723 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 777, 9723 is 21.
HCF(777, 9723) = 21
HCF of 777, 9723 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 777, 9723 is 21.
Highest Common Factor of 777,9723 is 21
Step 1: Since 9723 > 777, we apply the division lemma to 9723 and 777, to get
9723 = 777 x 12 + 399
Step 2: Since the reminder 777 ≠ 0, we apply division lemma to 399 and 777, to get
777 = 399 x 1 + 378
Step 3: We consider the new divisor 399 and the new remainder 378, and apply the division lemma to get
399 = 378 x 1 + 21
We consider the new divisor 378 and the new remainder 21, and apply the division lemma to get
378 = 21 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 777 and 9723 is 21
Notice that 21 = HCF(378,21) = HCF(399,378) = HCF(777,399) = HCF(9723,777) .
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Frequently Asked Questions on HCF of 777, 9723 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 777, 9723?
Answer: HCF of 777, 9723 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 777, 9723 using Euclid's Algorithm?
Answer: For arbitrary numbers 777, 9723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.