Highest Common Factor of 663, 546, 410 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 663, 546, 410 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 546, 410 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 663, 546, 410 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 663, 546, 410 is 1.
HCF(663, 546, 410) = 1
HCF of 663, 546, 410 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 546, 410 is 1.
Highest Common Factor of 663,546,410 is 1
Step 1: Since 663 > 546, we apply the division lemma to 663 and 546, to get
663 = 546 x 1 + 117
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 117 and 546, to get
546 = 117 x 4 + 78
Step 3: We consider the new divisor 117 and the new remainder 78, and apply the division lemma to get
117 = 78 x 1 + 39
We consider the new divisor 78 and the new remainder 39, and apply the division lemma to get
78 = 39 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 663 and 546 is 39
Notice that 39 = HCF(78,39) = HCF(117,78) = HCF(546,117) = HCF(663,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 410 > 39, we apply the division lemma to 410 and 39, to get
410 = 39 x 10 + 20
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 20 and 39, to get
39 = 20 x 1 + 19
Step 3: We consider the new divisor 20 and the new remainder 19, and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1, and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 39 and 410 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(410,39) .
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Frequently Asked Questions on HCF of 663, 546, 410 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 663, 546, 410?
Answer: HCF of 663, 546, 410 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 546, 410 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 546, 410 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
