Highest Common Factor of 642, 172, 435 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 642, 172, 435 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 172, 435 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 642, 172, 435 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 642, 172, 435 is 1.
HCF(642, 172, 435) = 1
HCF of 642, 172, 435 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 172, 435 is 1.
Highest Common Factor of 642,172,435 is 1
Step 1: Since 642 > 172, we apply the division lemma to 642 and 172, to get
642 = 172 x 3 + 126
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 126 and 172, to get
172 = 126 x 1 + 46
Step 3: We consider the new divisor 126 and the new remainder 46, and apply the division lemma to get
126 = 46 x 2 + 34
We consider the new divisor 46 and the new remainder 34,and apply the division lemma to get
46 = 34 x 1 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 642 and 172 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(46,34) = HCF(126,46) = HCF(172,126) = HCF(642,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 435 > 2, we apply the division lemma to 435 and 2, to get
435 = 2 x 217 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 435 is 1
Notice that 1 = HCF(2,1) = HCF(435,2) .
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Frequently Asked Questions on HCF of 642, 172, 435 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 642, 172, 435?
Answer: HCF of 642, 172, 435 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 172, 435 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 172, 435 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.