Highest Common Factor of 642, 457, 164 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, 457, 164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 457, 164 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, 457, 164 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, 457, 164 is 1.
HCF(642, 457, 164) = 1
HCF of 642, 457, 164 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, 457, 164 is 1.
Highest Common Factor of 642,457,164 is 1
Step 1: Since 642 > 457, we apply the division lemma to 642 and 457, to get
642 = 457 x 1 + 185
Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 185 and 457, to get
457 = 185 x 2 + 87
Step 3: We consider the new divisor 185 and the new remainder 87, and apply the division lemma to get
185 = 87 x 2 + 11
We consider the new divisor 87 and the new remainder 11,and apply the division lemma to get
87 = 11 x 7 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 642 and 457 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(87,11) = HCF(185,87) = HCF(457,185) = HCF(642,457) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 164 > 1, we apply the division lemma to 164 and 1, to get
164 = 1 x 164 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 164 is 1
Notice that 1 = HCF(164,1) .
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Frequently Asked Questions on HCF of 642, 457, 164 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, 457, 164?
Answer: HCF of 642, 457, 164 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 457, 164 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 457, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.