Highest Common Factor of 918, 135, 289 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 918, 135, 289 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 918, 135, 289 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 918, 135, 289 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 918, 135, 289 is 1.
HCF(918, 135, 289) = 1
HCF of 918, 135, 289 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 918, 135, 289 is 1.
Highest Common Factor of 918,135,289 is 1
Step 1: Since 918 > 135, we apply the division lemma to 918 and 135, to get
918 = 135 x 6 + 108
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 108 and 135, to get
135 = 108 x 1 + 27
Step 3: We consider the new divisor 108 and the new remainder 27, and apply the division lemma to get
108 = 27 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 918 and 135 is 27
Notice that 27 = HCF(108,27) = HCF(135,108) = HCF(918,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 289 > 27, we apply the division lemma to 289 and 27, to get
289 = 27 x 10 + 19
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 19 and 27, to get
27 = 19 x 1 + 8
Step 3: We consider the new divisor 19 and the new remainder 8, and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
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 27 and 289 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(289,27) .
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Frequently Asked Questions on HCF of 918, 135, 289 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 918, 135, 289?
Answer: HCF of 918, 135, 289 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 918, 135, 289 using Euclid's Algorithm?
Answer: For arbitrary numbers 918, 135, 289 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.