Highest Common Factor of 705, 188, 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 705, 188, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 188, 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 705, 188, 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 705, 188, 173 is 1.
HCF(705, 188, 173) = 1
HCF of 705, 188, 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 705, 188, 173 is 1.
Highest Common Factor of 705,188,173 is 1
Step 1: Since 705 > 188, we apply the division lemma to 705 and 188, to get
705 = 188 x 3 + 141
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 141 and 188, to get
188 = 141 x 1 + 47
Step 3: We consider the new divisor 141 and the new remainder 47, and apply the division lemma to get
141 = 47 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 47, the HCF of 705 and 188 is 47
Notice that 47 = HCF(141,47) = HCF(188,141) = HCF(705,188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 173 > 47, we apply the division lemma to 173 and 47, to get
173 = 47 x 3 + 32
Step 2: Since the reminder 47 ≠ 0, we apply division lemma to 32 and 47, to get
47 = 32 x 1 + 15
Step 3: We consider the new divisor 32 and the new remainder 15, and apply the division lemma to get
32 = 15 x 2 + 2
We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get
15 = 2 x 7 + 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 47 and 173 is 1
Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(32,15) = HCF(47,32) = HCF(173,47) .
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Frequently Asked Questions on HCF of 705, 188, 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 705, 188, 173?
Answer: HCF of 705, 188, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 188, 173 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 188, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.