Highest Common Factor of 557, 505 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, 505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 557, 505 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, 505 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, 505 is 1.
HCF(557, 505) = 1
HCF of 557, 505 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, 505 is 1.
Highest Common Factor of 557,505 is 1
Step 1: Since 557 > 505, we apply the division lemma to 557 and 505, to get
557 = 505 x 1 + 52
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 52 and 505, to get
505 = 52 x 9 + 37
Step 3: We consider the new divisor 52 and the new remainder 37, and apply the division lemma to get
52 = 37 x 1 + 15
We consider the new divisor 37 and the new remainder 15,and apply the division lemma to get
37 = 15 x 2 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 557 and 505 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(37,15) = HCF(52,37) = HCF(505,52) = HCF(557,505) .
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Frequently Asked Questions on HCF of 557, 505 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, 505?
Answer: HCF of 557, 505 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 557, 505 using Euclid's Algorithm?
Answer: For arbitrary numbers 557, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.