Highest Common Factor of 645, 178, 685, 173 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 645, 178, 685, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 178, 685, 173 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 645, 178, 685, 173 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 645, 178, 685, 173 is 1.
HCF(645, 178, 685, 173) = 1
HCF of 645, 178, 685, 173 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 178, 685, 173 is 1.
Highest Common Factor of 645,178,685,173 is 1
Step 1: Since 645 > 178, we apply the division lemma to 645 and 178, to get
645 = 178 x 3 + 111
Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 111 and 178, to get
178 = 111 x 1 + 67
Step 3: We consider the new divisor 111 and the new remainder 67, and apply the division lemma to get
111 = 67 x 1 + 44
We consider the new divisor 67 and the new remainder 44,and apply the division lemma to get
67 = 44 x 1 + 23
We consider the new divisor 44 and the new remainder 23,and apply the division lemma to get
44 = 23 x 1 + 21
We consider the new divisor 23 and the new remainder 21,and apply the division lemma to get
23 = 21 x 1 + 2
We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get
21 = 2 x 10 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 645 and 178 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(44,23) = HCF(67,44) = HCF(111,67) = HCF(178,111) = HCF(645,178) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 685 > 1, we apply the division lemma to 685 and 1, to get
685 = 1 x 685 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 685 is 1
Notice that 1 = HCF(685,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 173 > 1, we apply the division lemma to 173 and 1, to get
173 = 1 x 173 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 173 is 1
Notice that 1 = HCF(173,1) .
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Frequently Asked Questions on HCF of 645, 178, 685, 173 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 645, 178, 685, 173?
Answer: HCF of 645, 178, 685, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 178, 685, 173 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 178, 685, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.