Highest Common Factor of 417, 117 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, 117 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 417, 117 is 3 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, 117 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, 117 is 3.
HCF(417, 117) = 3
HCF of 417, 117 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, 117 is 3.
Highest Common Factor of 417,117 is 3
Step 1: Since 417 > 117, we apply the division lemma to 417 and 117, to get
417 = 117 x 3 + 66
Step 2: Since the reminder 117 ≠ 0, we apply division lemma to 66 and 117, to get
117 = 66 x 1 + 51
Step 3: We consider the new divisor 66 and the new remainder 51, and apply the division lemma to get
66 = 51 x 1 + 15
We consider the new divisor 51 and the new remainder 15,and apply the division lemma to get
51 = 15 x 3 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 417 and 117 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(51,15) = HCF(66,51) = HCF(117,66) = HCF(417,117) .
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Frequently Asked Questions on HCF of 417, 117 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, 117?
Answer: HCF of 417, 117 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 417, 117 using Euclid's Algorithm?
Answer: For arbitrary numbers 417, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.