Highest Common Factor of 289, 8023 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 289, 8023 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 289, 8023 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 289, 8023 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 289, 8023 is 1.
HCF(289, 8023) = 1
HCF of 289, 8023 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 289, 8023 is 1.
Highest Common Factor of 289,8023 is 1
Step 1: Since 8023 > 289, we apply the division lemma to 8023 and 289, to get
8023 = 289 x 27 + 220
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 220 and 289, to get
289 = 220 x 1 + 69
Step 3: We consider the new divisor 220 and the new remainder 69, and apply the division lemma to get
220 = 69 x 3 + 13
We consider the new divisor 69 and the new remainder 13,and apply the division lemma to get
69 = 13 x 5 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 289 and 8023 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(69,13) = HCF(220,69) = HCF(289,220) = HCF(8023,289) .
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Frequently Asked Questions on HCF of 289, 8023 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 289, 8023?
Answer: HCF of 289, 8023 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 289, 8023 using Euclid's Algorithm?
Answer: For arbitrary numbers 289, 8023 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.