Highest Common Factor of 354, 405, 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 354, 405, 463 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 405, 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 354, 405, 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 354, 405, 463 is 1.
HCF(354, 405, 463) = 1
HCF of 354, 405, 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 354, 405, 463 is 1.
Highest Common Factor of 354,405,463 is 1
Step 1: Since 405 > 354, we apply the division lemma to 405 and 354, to get
405 = 354 x 1 + 51
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 51 and 354, to get
354 = 51 x 6 + 48
Step 3: We consider the new divisor 51 and the new remainder 48, and apply the division lemma to get
51 = 48 x 1 + 3
We consider the new divisor 48 and the new remainder 3, and apply the division lemma to get
48 = 3 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 354 and 405 is 3
Notice that 3 = HCF(48,3) = HCF(51,48) = HCF(354,51) = HCF(405,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 463 > 3, we apply the division lemma to 463 and 3, to get
463 = 3 x 154 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 463 is 1
Notice that 1 = HCF(3,1) = HCF(463,3) .
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Frequently Asked Questions on HCF of 354, 405, 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 354, 405, 463?
Answer: HCF of 354, 405, 463 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 405, 463 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 405, 463 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.