Highest Common Factor of 210, 168, 563 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 210, 168, 563 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 168, 563 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 210, 168, 563 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 210, 168, 563 is 1.
HCF(210, 168, 563) = 1
HCF of 210, 168, 563 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 168, 563 is 1.
Highest Common Factor of 210,168,563 is 1
Step 1: Since 210 > 168, we apply the division lemma to 210 and 168, to get
210 = 168 x 1 + 42
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 42 and 168, to get
168 = 42 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 210 and 168 is 42
Notice that 42 = HCF(168,42) = HCF(210,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 563 > 42, we apply the division lemma to 563 and 42, to get
563 = 42 x 13 + 17
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 17 and 42, to get
42 = 17 x 2 + 8
Step 3: We consider the new divisor 17 and the new remainder 8, and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1, and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 42 and 563 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(42,17) = HCF(563,42) .
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Frequently Asked Questions on HCF of 210, 168, 563 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 210, 168, 563?
Answer: HCF of 210, 168, 563 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 168, 563 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 168, 563 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.