Highest Common Factor of 288, 123, 365, 589 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 288, 123, 365, 589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 123, 365, 589 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 288, 123, 365, 589 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 288, 123, 365, 589 is 1.
HCF(288, 123, 365, 589) = 1
HCF of 288, 123, 365, 589 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 288, 123, 365, 589 is 1.
Highest Common Factor of 288,123,365,589 is 1
Step 1: Since 288 > 123, we apply the division lemma to 288 and 123, to get
288 = 123 x 2 + 42
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 42 and 123, to get
123 = 42 x 2 + 39
Step 3: We consider the new divisor 42 and the new remainder 39, and apply the division lemma to get
42 = 39 x 1 + 3
We consider the new divisor 39 and the new remainder 3, and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 288 and 123 is 3
Notice that 3 = HCF(39,3) = HCF(42,39) = HCF(123,42) = HCF(288,123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 365 > 3, we apply the division lemma to 365 and 3, to get
365 = 3 x 121 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 365 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(365,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 589 > 1, we apply the division lemma to 589 and 1, to get
589 = 1 x 589 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 589 is 1
Notice that 1 = HCF(589,1) .
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Frequently Asked Questions on HCF of 288, 123, 365, 589 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 288, 123, 365, 589?
Answer: HCF of 288, 123, 365, 589 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 123, 365, 589 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 123, 365, 589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.