Highest Common Factor of 614, 990, 35, 259 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 614, 990, 35, 259 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 614, 990, 35, 259 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 614, 990, 35, 259 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 614, 990, 35, 259 is 1.
HCF(614, 990, 35, 259) = 1
HCF of 614, 990, 35, 259 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 614, 990, 35, 259 is 1.
Highest Common Factor of 614,990,35,259 is 1
Step 1: Since 990 > 614, we apply the division lemma to 990 and 614, to get
990 = 614 x 1 + 376
Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 376 and 614, to get
614 = 376 x 1 + 238
Step 3: We consider the new divisor 376 and the new remainder 238, and apply the division lemma to get
376 = 238 x 1 + 138
We consider the new divisor 238 and the new remainder 138,and apply the division lemma to get
238 = 138 x 1 + 100
We consider the new divisor 138 and the new remainder 100,and apply the division lemma to get
138 = 100 x 1 + 38
We consider the new divisor 100 and the new remainder 38,and apply the division lemma to get
100 = 38 x 2 + 24
We consider the new divisor 38 and the new remainder 24,and apply the division lemma to get
38 = 24 x 1 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 990 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(38,24) = HCF(100,38) = HCF(138,100) = HCF(238,138) = HCF(376,238) = HCF(614,376) = HCF(990,614) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35 > 2, we apply the division lemma to 35 and 2, to get
35 = 2 x 17 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 35 is 1
Notice that 1 = HCF(2,1) = HCF(35,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 259 > 1, we apply the division lemma to 259 and 1, to get
259 = 1 x 259 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 259 is 1
Notice that 1 = HCF(259,1) .
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Frequently Asked Questions on HCF of 614, 990, 35, 259 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 614, 990, 35, 259?
Answer: HCF of 614, 990, 35, 259 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 614, 990, 35, 259 using Euclid's Algorithm?
Answer: For arbitrary numbers 614, 990, 35, 259 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.