Highest Common Factor of 642, 188 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, 188 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 188 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 642, 188 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, 188 is 2.
HCF(642, 188) = 2
HCF of 642, 188 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, 188 is 2.
Highest Common Factor of 642,188 is 2
Step 1: Since 642 > 188, we apply the division lemma to 642 and 188, to get
642 = 188 x 3 + 78
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 78 and 188, to get
188 = 78 x 2 + 32
Step 3: We consider the new divisor 78 and the new remainder 32, and apply the division lemma to get
78 = 32 x 2 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 642 and 188 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(78,32) = HCF(188,78) = HCF(642,188) .
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Frequently Asked Questions on HCF of 642, 188 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, 188?
Answer: HCF of 642, 188 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 188 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.