Highest Common Factor of 176, 6100, 9217 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 176, 6100, 9217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 176, 6100, 9217 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 176, 6100, 9217 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 176, 6100, 9217 is 1.
HCF(176, 6100, 9217) = 1
HCF of 176, 6100, 9217 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 176, 6100, 9217 is 1.
Highest Common Factor of 176,6100,9217 is 1
Step 1: Since 6100 > 176, we apply the division lemma to 6100 and 176, to get
6100 = 176 x 34 + 116
Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 116 and 176, to get
176 = 116 x 1 + 60
Step 3: We consider the new divisor 116 and the new remainder 60, and apply the division lemma to get
116 = 60 x 1 + 56
We consider the new divisor 60 and the new remainder 56,and apply the division lemma to get
60 = 56 x 1 + 4
We consider the new divisor 56 and the new remainder 4,and apply the division lemma to get
56 = 4 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 176 and 6100 is 4
Notice that 4 = HCF(56,4) = HCF(60,56) = HCF(116,60) = HCF(176,116) = HCF(6100,176) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9217 > 4, we apply the division lemma to 9217 and 4, to get
9217 = 4 x 2304 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 9217 is 1
Notice that 1 = HCF(4,1) = HCF(9217,4) .
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Frequently Asked Questions on HCF of 176, 6100, 9217 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 176, 6100, 9217?
Answer: HCF of 176, 6100, 9217 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 176, 6100, 9217 using Euclid's Algorithm?
Answer: For arbitrary numbers 176, 6100, 9217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.