Highest Common Factor of 322, 9223 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 322, 9223 i.e. 23 the largest integer that leaves a remainder zero for all numbers.
HCF of 322, 9223 is 23 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 322, 9223 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 322, 9223 is 23.
HCF(322, 9223) = 23
HCF of 322, 9223 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 322, 9223 is 23.
Highest Common Factor of 322,9223 is 23
Step 1: Since 9223 > 322, we apply the division lemma to 9223 and 322, to get
9223 = 322 x 28 + 207
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 207 and 322, to get
322 = 207 x 1 + 115
Step 3: We consider the new divisor 207 and the new remainder 115, and apply the division lemma to get
207 = 115 x 1 + 92
We consider the new divisor 115 and the new remainder 92,and apply the division lemma to get
115 = 92 x 1 + 23
We consider the new divisor 92 and the new remainder 23,and apply the division lemma to get
92 = 23 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 322 and 9223 is 23
Notice that 23 = HCF(92,23) = HCF(115,92) = HCF(207,115) = HCF(322,207) = HCF(9223,322) .
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Frequently Asked Questions on HCF of 322, 9223 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 322, 9223?
Answer: HCF of 322, 9223 is 23 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 322, 9223 using Euclid's Algorithm?
Answer: For arbitrary numbers 322, 9223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.