Highest Common Factor of 598, 227, 315 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 598, 227, 315 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 598, 227, 315 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 598, 227, 315 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 598, 227, 315 is 1.
HCF(598, 227, 315) = 1
HCF of 598, 227, 315 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 598, 227, 315 is 1.
Highest Common Factor of 598,227,315 is 1
Step 1: Since 598 > 227, we apply the division lemma to 598 and 227, to get
598 = 227 x 2 + 144
Step 2: Since the reminder 227 ≠ 0, we apply division lemma to 144 and 227, to get
227 = 144 x 1 + 83
Step 3: We consider the new divisor 144 and the new remainder 83, and apply the division lemma to get
144 = 83 x 1 + 61
We consider the new divisor 83 and the new remainder 61,and apply the division lemma to get
83 = 61 x 1 + 22
We consider the new divisor 61 and the new remainder 22,and apply the division lemma to get
61 = 22 x 2 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 598 and 227 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) = HCF(83,61) = HCF(144,83) = HCF(227,144) = HCF(598,227) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 315 > 1, we apply the division lemma to 315 and 1, to get
315 = 1 x 315 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 315 is 1
Notice that 1 = HCF(315,1) .
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Frequently Asked Questions on HCF of 598, 227, 315 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 598, 227, 315?
Answer: HCF of 598, 227, 315 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 598, 227, 315 using Euclid's Algorithm?
Answer: For arbitrary numbers 598, 227, 315 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
