Highest Common Factor of 408, 253, 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 408, 253, 563 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 253, 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 408, 253, 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 408, 253, 563 is 1.
HCF(408, 253, 563) = 1
HCF of 408, 253, 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 408, 253, 563 is 1.
Highest Common Factor of 408,253,563 is 1
Step 1: Since 408 > 253, we apply the division lemma to 408 and 253, to get
408 = 253 x 1 + 155
Step 2: Since the reminder 253 ≠ 0, we apply division lemma to 155 and 253, to get
253 = 155 x 1 + 98
Step 3: We consider the new divisor 155 and the new remainder 98, and apply the division lemma to get
155 = 98 x 1 + 57
We consider the new divisor 98 and the new remainder 57,and apply the division lemma to get
98 = 57 x 1 + 41
We consider the new divisor 57 and the new remainder 41,and apply the division lemma to get
57 = 41 x 1 + 16
We consider the new divisor 41 and the new remainder 16,and apply the division lemma to get
41 = 16 x 2 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 408 and 253 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(41,16) = HCF(57,41) = HCF(98,57) = HCF(155,98) = HCF(253,155) = HCF(408,253) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 563 > 1, we apply the division lemma to 563 and 1, to get
563 = 1 x 563 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 563 is 1
Notice that 1 = HCF(563,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 408, 253, 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 408, 253, 563?
Answer: HCF of 408, 253, 563 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 253, 563 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 253, 563 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
