Highest Common Factor of 205, 340, 288 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 205, 340, 288 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 205, 340, 288 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 205, 340, 288 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 205, 340, 288 is 1.
HCF(205, 340, 288) = 1
HCF of 205, 340, 288 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 205, 340, 288 is 1.
Highest Common Factor of 205,340,288 is 1
Step 1: Since 340 > 205, we apply the division lemma to 340 and 205, to get
340 = 205 x 1 + 135
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 135 and 205, to get
205 = 135 x 1 + 70
Step 3: We consider the new divisor 135 and the new remainder 70, and apply the division lemma to get
135 = 70 x 1 + 65
We consider the new divisor 70 and the new remainder 65,and apply the division lemma to get
70 = 65 x 1 + 5
We consider the new divisor 65 and the new remainder 5,and apply the division lemma to get
65 = 5 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 205 and 340 is 5
Notice that 5 = HCF(65,5) = HCF(70,65) = HCF(135,70) = HCF(205,135) = HCF(340,205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 288 > 5, we apply the division lemma to 288 and 5, to get
288 = 5 x 57 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 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 5 and 288 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(288,5) .
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Frequently Asked Questions on HCF of 205, 340, 288 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 205, 340, 288?
Answer: HCF of 205, 340, 288 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 205, 340, 288 using Euclid's Algorithm?
Answer: For arbitrary numbers 205, 340, 288 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.