Highest Common Factor of 784, 9123 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 784, 9123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 9123 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 784, 9123 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 784, 9123 is 1.
HCF(784, 9123) = 1
HCF of 784, 9123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 784, 9123 is 1.
Highest Common Factor of 784,9123 is 1
Step 1: Since 9123 > 784, we apply the division lemma to 9123 and 784, to get
9123 = 784 x 11 + 499
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 499 and 784, to get
784 = 499 x 1 + 285
Step 3: We consider the new divisor 499 and the new remainder 285, and apply the division lemma to get
499 = 285 x 1 + 214
We consider the new divisor 285 and the new remainder 214,and apply the division lemma to get
285 = 214 x 1 + 71
We consider the new divisor 214 and the new remainder 71,and apply the division lemma to get
214 = 71 x 3 + 1
We consider the new divisor 71 and the new remainder 1,and apply the division lemma to get
71 = 1 x 71 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 784 and 9123 is 1
Notice that 1 = HCF(71,1) = HCF(214,71) = HCF(285,214) = HCF(499,285) = HCF(784,499) = HCF(9123,784) .
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Frequently Asked Questions on HCF of 784, 9123 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 784, 9123?
Answer: HCF of 784, 9123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 9123 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 9123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.