Highest Common Factor of 402, 654, 432 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 402, 654, 432 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 654, 432 is 6 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 402, 654, 432 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 402, 654, 432 is 6.
HCF(402, 654, 432) = 6
HCF of 402, 654, 432 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 402, 654, 432 is 6.
Highest Common Factor of 402,654,432 is 6
Step 1: Since 654 > 402, we apply the division lemma to 654 and 402, to get
654 = 402 x 1 + 252
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 252 and 402, to get
402 = 252 x 1 + 150
Step 3: We consider the new divisor 252 and the new remainder 150, and apply the division lemma to get
252 = 150 x 1 + 102
We consider the new divisor 150 and the new remainder 102,and apply the division lemma to get
150 = 102 x 1 + 48
We consider the new divisor 102 and the new remainder 48,and apply the division lemma to get
102 = 48 x 2 + 6
We consider the new divisor 48 and the new remainder 6,and apply the division lemma to get
48 = 6 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 402 and 654 is 6
Notice that 6 = HCF(48,6) = HCF(102,48) = HCF(150,102) = HCF(252,150) = HCF(402,252) = HCF(654,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 432 > 6, we apply the division lemma to 432 and 6, to get
432 = 6 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 432 is 6
Notice that 6 = HCF(432,6) .
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Frequently Asked Questions on HCF of 402, 654, 432 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 402, 654, 432?
Answer: HCF of 402, 654, 432 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 654, 432 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 654, 432 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.