Highest Common Factor of 289, 391, 31 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, 391, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 289, 391, 31 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, 391, 31 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, 391, 31 is 1.
HCF(289, 391, 31) = 1
HCF of 289, 391, 31 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, 391, 31 is 1.
Highest Common Factor of 289,391,31 is 1
Step 1: Since 391 > 289, we apply the division lemma to 391 and 289, to get
391 = 289 x 1 + 102
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 102 and 289, to get
289 = 102 x 2 + 85
Step 3: We consider the new divisor 102 and the new remainder 85, and apply the division lemma to get
102 = 85 x 1 + 17
We consider the new divisor 85 and the new remainder 17, and apply the division lemma to get
85 = 17 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 289 and 391 is 17
Notice that 17 = HCF(85,17) = HCF(102,85) = HCF(289,102) = HCF(391,289) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 17, we apply the division lemma to 31 and 17, to get
31 = 17 x 1 + 14
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 14 and 17, to get
17 = 14 x 1 + 3
Step 3: We consider the new divisor 14 and the new remainder 3, and apply the division lemma to get
14 = 3 x 4 + 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 17 and 31 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) .
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Frequently Asked Questions on HCF of 289, 391, 31 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, 391, 31?
Answer: HCF of 289, 391, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 289, 391, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 289, 391, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.