Highest Common Factor of 650, 172, 417 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 650, 172, 417 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 650, 172, 417 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 650, 172, 417 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 650, 172, 417 is 1.
HCF(650, 172, 417) = 1
HCF of 650, 172, 417 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 650, 172, 417 is 1.
Highest Common Factor of 650,172,417 is 1
Step 1: Since 650 > 172, we apply the division lemma to 650 and 172, to get
650 = 172 x 3 + 134
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 134 and 172, to get
172 = 134 x 1 + 38
Step 3: We consider the new divisor 134 and the new remainder 38, and apply the division lemma to get
134 = 38 x 3 + 20
We consider the new divisor 38 and the new remainder 20,and apply the division lemma to get
38 = 20 x 1 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 650 and 172 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(38,20) = HCF(134,38) = HCF(172,134) = HCF(650,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 417 > 2, we apply the division lemma to 417 and 2, to get
417 = 2 x 208 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 417 is 1
Notice that 1 = HCF(2,1) = HCF(417,2) .
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Frequently Asked Questions on HCF of 650, 172, 417 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 650, 172, 417?
Answer: HCF of 650, 172, 417 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 650, 172, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 650, 172, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.