Highest Common Factor of 642, 9514 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 642, 9514 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 9514 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 642, 9514 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 642, 9514 is 2.
HCF(642, 9514) = 2
HCF of 642, 9514 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 9514 is 2.
Highest Common Factor of 642,9514 is 2
Step 1: Since 9514 > 642, we apply the division lemma to 9514 and 642, to get
9514 = 642 x 14 + 526
Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 526 and 642, to get
642 = 526 x 1 + 116
Step 3: We consider the new divisor 526 and the new remainder 116, and apply the division lemma to get
526 = 116 x 4 + 62
We consider the new divisor 116 and the new remainder 62,and apply the division lemma to get
116 = 62 x 1 + 54
We consider the new divisor 62 and the new remainder 54,and apply the division lemma to get
62 = 54 x 1 + 8
We consider the new divisor 54 and the new remainder 8,and apply the division lemma to get
54 = 8 x 6 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 642 and 9514 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(54,8) = HCF(62,54) = HCF(116,62) = HCF(526,116) = HCF(642,526) = HCF(9514,642) .
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Frequently Asked Questions on HCF of 642, 9514 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 642, 9514?
Answer: HCF of 642, 9514 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 9514 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 9514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.