Highest Common Factor of 177, 123, 163 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 177, 123, 163 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 177, 123, 163 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 177, 123, 163 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 177, 123, 163 is 1.
HCF(177, 123, 163) = 1
HCF of 177, 123, 163 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 177, 123, 163 is 1.
Highest Common Factor of 177,123,163 is 1
Step 1: Since 177 > 123, we apply the division lemma to 177 and 123, to get
177 = 123 x 1 + 54
Step 2: Since the reminder 123 ≠ 0, we apply division lemma to 54 and 123, to get
123 = 54 x 2 + 15
Step 3: We consider the new divisor 54 and the new remainder 15, and apply the division lemma to get
54 = 15 x 3 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 177 and 123 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(123,54) = HCF(177,123) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 163 > 3, we apply the division lemma to 163 and 3, to get
163 = 3 x 54 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 163 is 1
Notice that 1 = HCF(3,1) = HCF(163,3) .
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Frequently Asked Questions on HCF of 177, 123, 163 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 177, 123, 163?
Answer: HCF of 177, 123, 163 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 177, 123, 163 using Euclid's Algorithm?
Answer: For arbitrary numbers 177, 123, 163 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.