Highest Common Factor of 560, 1277 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 560, 1277 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 1277 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 560, 1277 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 560, 1277 is 1.
HCF(560, 1277) = 1
HCF of 560, 1277 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 560, 1277 is 1.
Highest Common Factor of 560,1277 is 1
Step 1: Since 1277 > 560, we apply the division lemma to 1277 and 560, to get
1277 = 560 x 2 + 157
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 157 and 560, to get
560 = 157 x 3 + 89
Step 3: We consider the new divisor 157 and the new remainder 89, and apply the division lemma to get
157 = 89 x 1 + 68
We consider the new divisor 89 and the new remainder 68,and apply the division lemma to get
89 = 68 x 1 + 21
We consider the new divisor 68 and the new remainder 21,and apply the division lemma to get
68 = 21 x 3 + 5
We consider the new divisor 21 and the new remainder 5,and apply the division lemma to get
21 = 5 x 4 + 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 560 and 1277 is 1
Notice that 1 = HCF(5,1) = HCF(21,5) = HCF(68,21) = HCF(89,68) = HCF(157,89) = HCF(560,157) = HCF(1277,560) .
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Frequently Asked Questions on HCF of 560, 1277 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 560, 1277?
Answer: HCF of 560, 1277 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 1277 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 1277 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.