Highest Common Factor of 563, 6007, 2154 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 563, 6007, 2154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 563, 6007, 2154 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 563, 6007, 2154 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 563, 6007, 2154 is 1.
HCF(563, 6007, 2154) = 1
HCF of 563, 6007, 2154 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 563, 6007, 2154 is 1.
Highest Common Factor of 563,6007,2154 is 1
Step 1: Since 6007 > 563, we apply the division lemma to 6007 and 563, to get
6007 = 563 x 10 + 377
Step 2: Since the reminder 563 ≠ 0, we apply division lemma to 377 and 563, to get
563 = 377 x 1 + 186
Step 3: We consider the new divisor 377 and the new remainder 186, and apply the division lemma to get
377 = 186 x 2 + 5
We consider the new divisor 186 and the new remainder 5,and apply the division lemma to get
186 = 5 x 37 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 563 and 6007 is 1
Notice that 1 = HCF(5,1) = HCF(186,5) = HCF(377,186) = HCF(563,377) = HCF(6007,563) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2154 > 1, we apply the division lemma to 2154 and 1, to get
2154 = 1 x 2154 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2154 is 1
Notice that 1 = HCF(2154,1) .
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Frequently Asked Questions on HCF of 563, 6007, 2154 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 563, 6007, 2154?
Answer: HCF of 563, 6007, 2154 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 563, 6007, 2154 using Euclid's Algorithm?
Answer: For arbitrary numbers 563, 6007, 2154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.