Highest Common Factor of 75, 171, 864, 127 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 75, 171, 864, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 75, 171, 864, 127 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 75, 171, 864, 127 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 75, 171, 864, 127 is 1.
HCF(75, 171, 864, 127) = 1
HCF of 75, 171, 864, 127 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 75, 171, 864, 127 is 1.
Highest Common Factor of 75,171,864,127 is 1
Step 1: Since 171 > 75, we apply the division lemma to 171 and 75, to get
171 = 75 x 2 + 21
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 21 and 75, to get
75 = 21 x 3 + 12
Step 3: We consider the new divisor 21 and the new remainder 12, and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 75 and 171 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(75,21) = HCF(171,75) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 864 > 3, we apply the division lemma to 864 and 3, to get
864 = 3 x 288 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 864 is 3
Notice that 3 = HCF(864,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 127 > 3, we apply the division lemma to 127 and 3, to get
127 = 3 x 42 + 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 127 is 1
Notice that 1 = HCF(3,1) = HCF(127,3) .
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Frequently Asked Questions on HCF of 75, 171, 864, 127 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 75, 171, 864, 127?
Answer: HCF of 75, 171, 864, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 75, 171, 864, 127 using Euclid's Algorithm?
Answer: For arbitrary numbers 75, 171, 864, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.