Highest Common Factor of 662, 546, 509 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, 546, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 662, 546, 509 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 662, 546, 509 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, 546, 509 is 1.
HCF(662, 546, 509) = 1
HCF of 662, 546, 509 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, 546, 509 is 1.
Highest Common Factor of 662,546,509 is 1
Step 1: Since 662 > 546, we apply the division lemma to 662 and 546, to get
662 = 546 x 1 + 116
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 116 and 546, to get
546 = 116 x 4 + 82
Step 3: We consider the new divisor 116 and the new remainder 82, and apply the division lemma to get
116 = 82 x 1 + 34
We consider the new divisor 82 and the new remainder 34,and apply the division lemma to get
82 = 34 x 2 + 14
We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get
34 = 14 x 2 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 546 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(82,34) = HCF(116,82) = HCF(546,116) = HCF(662,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 509 > 2, we apply the division lemma to 509 and 2, to get
509 = 2 x 254 + 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 509 is 1
Notice that 1 = HCF(2,1) = HCF(509,2) .
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Frequently Asked Questions on HCF of 662, 546, 509 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, 546, 509?
Answer: HCF of 662, 546, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 662, 546, 509 using Euclid's Algorithm?
Answer: For arbitrary numbers 662, 546, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.