Highest Common Factor of 111, 302, 559 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 111, 302, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 111, 302, 559 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 111, 302, 559 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 111, 302, 559 is 1.
HCF(111, 302, 559) = 1
HCF of 111, 302, 559 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 111, 302, 559 is 1.
Highest Common Factor of 111,302,559 is 1
Step 1: Since 302 > 111, we apply the division lemma to 302 and 111, to get
302 = 111 x 2 + 80
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 80 and 111, to get
111 = 80 x 1 + 31
Step 3: We consider the new divisor 80 and the new remainder 31, and apply the division lemma to get
80 = 31 x 2 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 111 and 302 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(80,31) = HCF(111,80) = HCF(302,111) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 559 > 1, we apply the division lemma to 559 and 1, to get
559 = 1 x 559 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 559 is 1
Notice that 1 = HCF(559,1) .
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Frequently Asked Questions on HCF of 111, 302, 559 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 111, 302, 559?
Answer: HCF of 111, 302, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 111, 302, 559 using Euclid's Algorithm?
Answer: For arbitrary numbers 111, 302, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.