Highest Common Factor of 562, 202, 17 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 562, 202, 17 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 562, 202, 17 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 562, 202, 17 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 562, 202, 17 is 1.
HCF(562, 202, 17) = 1
HCF of 562, 202, 17 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 562, 202, 17 is 1.
Highest Common Factor of 562,202,17 is 1
Step 1: Since 562 > 202, we apply the division lemma to 562 and 202, to get
562 = 202 x 2 + 158
Step 2: Since the reminder 202 ≠ 0, we apply division lemma to 158 and 202, to get
202 = 158 x 1 + 44
Step 3: We consider the new divisor 158 and the new remainder 44, and apply the division lemma to get
158 = 44 x 3 + 26
We consider the new divisor 44 and the new remainder 26,and apply the division lemma to get
44 = 26 x 1 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 562 and 202 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(44,26) = HCF(158,44) = HCF(202,158) = HCF(562,202) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 17 > 2, we apply the division lemma to 17 and 2, to get
17 = 2 x 8 + 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 17 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) .
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Frequently Asked Questions on HCF of 562, 202, 17 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 562, 202, 17?
Answer: HCF of 562, 202, 17 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 562, 202, 17 using Euclid's Algorithm?
Answer: For arbitrary numbers 562, 202, 17 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.