Highest Common Factor of 417, 164, 72 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 417, 164, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 164, 72 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 417, 164, 72 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 417, 164, 72 is 1.
HCF(417, 164, 72) = 1
HCF of 417, 164, 72 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 417, 164, 72 is 1.
Highest Common Factor of 417,164,72 is 1
Step 1: Since 417 > 164, we apply the division lemma to 417 and 164, to get
417 = 164 x 2 + 89
Step 2: Since the reminder 164 ≠ 0, we apply division lemma to 89 and 164, to get
164 = 89 x 1 + 75
Step 3: We consider the new divisor 89 and the new remainder 75, and apply the division lemma to get
89 = 75 x 1 + 14
We consider the new divisor 75 and the new remainder 14,and apply the division lemma to get
75 = 14 x 5 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 417 and 164 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(75,14) = HCF(89,75) = HCF(164,89) = HCF(417,164) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get
72 = 1 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1
Notice that 1 = HCF(72,1) .
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Frequently Asked Questions on HCF of 417, 164, 72 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 417, 164, 72?
Answer: HCF of 417, 164, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 164, 72 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 164, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.