Highest Common Factor of 414, 174, 217 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 414, 174, 217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 174, 217 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 414, 174, 217 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 414, 174, 217 is 1.
HCF(414, 174, 217) = 1
HCF of 414, 174, 217 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 174, 217 is 1.
Highest Common Factor of 414,174,217 is 1
Step 1: Since 414 > 174, we apply the division lemma to 414 and 174, to get
414 = 174 x 2 + 66
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 66 and 174, to get
174 = 66 x 2 + 42
Step 3: We consider the new divisor 66 and the new remainder 42, and apply the division lemma to get
66 = 42 x 1 + 24
We consider the new divisor 42 and the new remainder 24,and apply the division lemma to get
42 = 24 x 1 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 414 and 174 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(66,42) = HCF(174,66) = HCF(414,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 217 > 6, we apply the division lemma to 217 and 6, to get
217 = 6 x 36 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 217 is 1
Notice that 1 = HCF(6,1) = HCF(217,6) .
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Frequently Asked Questions on HCF of 414, 174, 217 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 414, 174, 217?
Answer: HCF of 414, 174, 217 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 174, 217 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 174, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.