Highest Common Factor of 199, 78, 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 199, 78, 417 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 199, 78, 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 199, 78, 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 199, 78, 417 is 1.
HCF(199, 78, 417) = 1
HCF of 199, 78, 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 199, 78, 417 is 1.
Highest Common Factor of 199,78,417 is 1
Step 1: Since 199 > 78, we apply the division lemma to 199 and 78, to get
199 = 78 x 2 + 43
Step 2: Since the reminder 78 ≠ 0, we apply division lemma to 43 and 78, to get
78 = 43 x 1 + 35
Step 3: We consider the new divisor 43 and the new remainder 35, and apply the division lemma to get
43 = 35 x 1 + 8
We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get
35 = 8 x 4 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 199 and 78 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(43,35) = HCF(78,43) = HCF(199,78) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 417 > 1, we apply the division lemma to 417 and 1, to get
417 = 1 x 417 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 417 is 1
Notice that 1 = HCF(417,1) .
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Frequently Asked Questions on HCF of 199, 78, 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 199, 78, 417?
Answer: HCF of 199, 78, 417 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 199, 78, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 199, 78, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.