Highest Common Factor of 289, 364 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, 364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 289, 364 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, 364 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, 364 is 1.
HCF(289, 364) = 1
HCF of 289, 364 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, 364 is 1.
Highest Common Factor of 289,364 is 1
Step 1: Since 364 > 289, we apply the division lemma to 364 and 289, to get
364 = 289 x 1 + 75
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 75 and 289, to get
289 = 75 x 3 + 64
Step 3: We consider the new divisor 75 and the new remainder 64, and apply the division lemma to get
75 = 64 x 1 + 11
We consider the new divisor 64 and the new remainder 11,and apply the division lemma to get
64 = 11 x 5 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 289 and 364 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(64,11) = HCF(75,64) = HCF(289,75) = HCF(364,289) .
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Frequently Asked Questions on HCF of 289, 364 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, 364?
Answer: HCF of 289, 364 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 289, 364 using Euclid's Algorithm?
Answer: For arbitrary numbers 289, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.