Highest Common Factor of 434, 740, 96 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 434, 740, 96 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 434, 740, 96 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 434, 740, 96 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 434, 740, 96 is 2.
HCF(434, 740, 96) = 2
HCF of 434, 740, 96 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 434, 740, 96 is 2.
Highest Common Factor of 434,740,96 is 2
Step 1: Since 740 > 434, we apply the division lemma to 740 and 434, to get
740 = 434 x 1 + 306
Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 306 and 434, to get
434 = 306 x 1 + 128
Step 3: We consider the new divisor 306 and the new remainder 128, and apply the division lemma to get
306 = 128 x 2 + 50
We consider the new divisor 128 and the new remainder 50,and apply the division lemma to get
128 = 50 x 2 + 28
We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get
50 = 28 x 1 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 434 and 740 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(128,50) = HCF(306,128) = HCF(434,306) = HCF(740,434) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96 > 2, we apply the division lemma to 96 and 2, to get
96 = 2 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 96 is 2
Notice that 2 = HCF(96,2) .
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Frequently Asked Questions on HCF of 434, 740, 96 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 434, 740, 96?
Answer: HCF of 434, 740, 96 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 434, 740, 96 using Euclid's Algorithm?
Answer: For arbitrary numbers 434, 740, 96 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
