Highest Common Factor of 432, 772, 334 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 432, 772, 334 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 772, 334 is 2 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 432, 772, 334 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 432, 772, 334 is 2.
HCF(432, 772, 334) = 2
HCF of 432, 772, 334 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 432, 772, 334 is 2.
Highest Common Factor of 432,772,334 is 2
Step 1: Since 772 > 432, we apply the division lemma to 772 and 432, to get
772 = 432 x 1 + 340
Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 340 and 432, to get
432 = 340 x 1 + 92
Step 3: We consider the new divisor 340 and the new remainder 92, and apply the division lemma to get
340 = 92 x 3 + 64
We consider the new divisor 92 and the new remainder 64,and apply the division lemma to get
92 = 64 x 1 + 28
We consider the new divisor 64 and the new remainder 28,and apply the division lemma to get
64 = 28 x 2 + 8
We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get
28 = 8 x 3 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 432 and 772 is 4
Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(64,28) = HCF(92,64) = HCF(340,92) = HCF(432,340) = HCF(772,432) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 334 > 4, we apply the division lemma to 334 and 4, to get
334 = 4 x 83 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 334 is 2
Notice that 2 = HCF(4,2) = HCF(334,4) .
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Frequently Asked Questions on HCF of 432, 772, 334 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 432, 772, 334?
Answer: HCF of 432, 772, 334 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 772, 334 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 772, 334 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.