Highest Common Factor of 557, 7178 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 557, 7178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 557, 7178 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 557, 7178 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 557, 7178 is 1.
HCF(557, 7178) = 1
HCF of 557, 7178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 557, 7178 is 1.
Highest Common Factor of 557,7178 is 1
Step 1: Since 7178 > 557, we apply the division lemma to 7178 and 557, to get
7178 = 557 x 12 + 494
Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 494 and 557, to get
557 = 494 x 1 + 63
Step 3: We consider the new divisor 494 and the new remainder 63, and apply the division lemma to get
494 = 63 x 7 + 53
We consider the new divisor 63 and the new remainder 53,and apply the division lemma to get
63 = 53 x 1 + 10
We consider the new divisor 53 and the new remainder 10,and apply the division lemma to get
53 = 10 x 5 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 7178 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(53,10) = HCF(63,53) = HCF(494,63) = HCF(557,494) = HCF(7178,557) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 557, 7178 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 557, 7178?
Answer: HCF of 557, 7178 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 557, 7178 using Euclid's Algorithm?
Answer: For arbitrary numbers 557, 7178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.