Highest Common Factor of 7543, 8177 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 7543, 8177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7543, 8177 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 7543, 8177 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 7543, 8177 is 1.
HCF(7543, 8177) = 1
HCF of 7543, 8177 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7543, 8177 is 1.
Highest Common Factor of 7543,8177 is 1
Step 1: Since 8177 > 7543, we apply the division lemma to 8177 and 7543, to get
8177 = 7543 x 1 + 634
Step 2: Since the reminder 7543 ≠ 0, we apply division lemma to 634 and 7543, to get
7543 = 634 x 11 + 569
Step 3: We consider the new divisor 634 and the new remainder 569, and apply the division lemma to get
634 = 569 x 1 + 65
We consider the new divisor 569 and the new remainder 65,and apply the division lemma to get
569 = 65 x 8 + 49
We consider the new divisor 65 and the new remainder 49,and apply the division lemma to get
65 = 49 x 1 + 16
We consider the new divisor 49 and the new remainder 16,and apply the division lemma to get
49 = 16 x 3 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7543 and 8177 is 1
Notice that 1 = HCF(16,1) = HCF(49,16) = HCF(65,49) = HCF(569,65) = HCF(634,569) = HCF(7543,634) = HCF(8177,7543) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7543, 8177 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 7543, 8177?
Answer: HCF of 7543, 8177 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7543, 8177 using Euclid's Algorithm?
Answer: For arbitrary numbers 7543, 8177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.