Highest Common Factor of 289, 1985, 2310 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, 1985, 2310 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 289, 1985, 2310 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, 1985, 2310 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, 1985, 2310 is 1.
HCF(289, 1985, 2310) = 1
HCF of 289, 1985, 2310 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, 1985, 2310 is 1.
Highest Common Factor of 289,1985,2310 is 1
Step 1: Since 1985 > 289, we apply the division lemma to 1985 and 289, to get
1985 = 289 x 6 + 251
Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 251 and 289, to get
289 = 251 x 1 + 38
Step 3: We consider the new divisor 251 and the new remainder 38, and apply the division lemma to get
251 = 38 x 6 + 23
We consider the new divisor 38 and the new remainder 23,and apply the division lemma to get
38 = 23 x 1 + 15
We consider the new divisor 23 and the new remainder 15,and apply the division lemma to get
23 = 15 x 1 + 8
We consider the new divisor 15 and the new remainder 8,and apply the division lemma to get
15 = 8 x 1 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 289 and 1985 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(23,15) = HCF(38,23) = HCF(251,38) = HCF(289,251) = HCF(1985,289) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2310 > 1, we apply the division lemma to 2310 and 1, to get
2310 = 1 x 2310 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2310 is 1
Notice that 1 = HCF(2310,1) .
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Frequently Asked Questions on HCF of 289, 1985, 2310 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, 1985, 2310?
Answer: HCF of 289, 1985, 2310 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 289, 1985, 2310 using Euclid's Algorithm?
Answer: For arbitrary numbers 289, 1985, 2310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.