Highest Common Factor of 614, 994 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, 994 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 614, 994 is 2 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, 994 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, 994 is 2.
HCF(614, 994) = 2
HCF of 614, 994 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, 994 is 2.
Highest Common Factor of 614,994 is 2
Step 1: Since 994 > 614, we apply the division lemma to 994 and 614, to get
994 = 614 x 1 + 380
Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 380 and 614, to get
614 = 380 x 1 + 234
Step 3: We consider the new divisor 380 and the new remainder 234, and apply the division lemma to get
380 = 234 x 1 + 146
We consider the new divisor 234 and the new remainder 146,and apply the division lemma to get
234 = 146 x 1 + 88
We consider the new divisor 146 and the new remainder 88,and apply the division lemma to get
146 = 88 x 1 + 58
We consider the new divisor 88 and the new remainder 58,and apply the division lemma to get
88 = 58 x 1 + 30
We consider the new divisor 58 and the new remainder 30,and apply the division lemma to get
58 = 30 x 1 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 994 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(58,30) = HCF(88,58) = HCF(146,88) = HCF(234,146) = HCF(380,234) = HCF(614,380) = HCF(994,614) .
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Frequently Asked Questions on HCF of 614, 994 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, 994?
Answer: HCF of 614, 994 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 614, 994 using Euclid's Algorithm?
Answer: For arbitrary numbers 614, 994 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.