Highest Common Factor of 662, 19618 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 662, 19618 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 19618 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 662, 19618 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 662, 19618 is 2.
HCF(662, 19618) = 2
HCF of 662, 19618 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 662, 19618 is 2.
Highest Common Factor of 662,19618 is 2
Step 1: Since 19618 > 662, we apply the division lemma to 19618 and 662, to get
19618 = 662 x 29 + 420
Step 2: Since the reminder 662 ≠ 0, we apply division lemma to 420 and 662, to get
662 = 420 x 1 + 242
Step 3: We consider the new divisor 420 and the new remainder 242, and apply the division lemma to get
420 = 242 x 1 + 178
We consider the new divisor 242 and the new remainder 178,and apply the division lemma to get
242 = 178 x 1 + 64
We consider the new divisor 178 and the new remainder 64,and apply the division lemma to get
178 = 64 x 2 + 50
We consider the new divisor 64 and the new remainder 50,and apply the division lemma to get
64 = 50 x 1 + 14
We consider the new divisor 50 and the new remainder 14,and apply the division lemma to get
50 = 14 x 3 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 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 662 and 19618 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(50,14) = HCF(64,50) = HCF(178,64) = HCF(242,178) = HCF(420,242) = HCF(662,420) = HCF(19618,662) .
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Frequently Asked Questions on HCF of 662, 19618 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 662, 19618?
Answer: HCF of 662, 19618 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 19618 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 19618 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.