Highest Common Factor of 405, 657, 463 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 405, 657, 463 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 657, 463 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 405, 657, 463 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 405, 657, 463 is 1.
HCF(405, 657, 463) = 1
HCF of 405, 657, 463 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 657, 463 is 1.
Highest Common Factor of 405,657,463 is 1
Step 1: Since 657 > 405, we apply the division lemma to 657 and 405, to get
657 = 405 x 1 + 252
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 252 and 405, to get
405 = 252 x 1 + 153
Step 3: We consider the new divisor 252 and the new remainder 153, and apply the division lemma to get
252 = 153 x 1 + 99
We consider the new divisor 153 and the new remainder 99,and apply the division lemma to get
153 = 99 x 1 + 54
We consider the new divisor 99 and the new remainder 54,and apply the division lemma to get
99 = 54 x 1 + 45
We consider the new divisor 54 and the new remainder 45,and apply the division lemma to get
54 = 45 x 1 + 9
We consider the new divisor 45 and the new remainder 9,and apply the division lemma to get
45 = 9 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 405 and 657 is 9
Notice that 9 = HCF(45,9) = HCF(54,45) = HCF(99,54) = HCF(153,99) = HCF(252,153) = HCF(405,252) = HCF(657,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 463 > 9, we apply the division lemma to 463 and 9, to get
463 = 9 x 51 + 4
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 4 and 9, to get
9 = 4 x 2 + 1
Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 463 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(463,9) .
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Frequently Asked Questions on HCF of 405, 657, 463 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 405, 657, 463?
Answer: HCF of 405, 657, 463 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 657, 463 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 657, 463 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.