Highest Common Factor of 560, 977, 882 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, 977, 882 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 977, 882 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, 977, 882 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, 977, 882 is 1.
HCF(560, 977, 882) = 1
HCF of 560, 977, 882 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, 977, 882 is 1.
Highest Common Factor of 560,977,882 is 1
Step 1: Since 977 > 560, we apply the division lemma to 977 and 560, to get
977 = 560 x 1 + 417
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 417 and 560, to get
560 = 417 x 1 + 143
Step 3: We consider the new divisor 417 and the new remainder 143, and apply the division lemma to get
417 = 143 x 2 + 131
We consider the new divisor 143 and the new remainder 131,and apply the division lemma to get
143 = 131 x 1 + 12
We consider the new divisor 131 and the new remainder 12,and apply the division lemma to get
131 = 12 x 10 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 560 and 977 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(131,12) = HCF(143,131) = HCF(417,143) = HCF(560,417) = HCF(977,560) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 882 > 1, we apply the division lemma to 882 and 1, to get
882 = 1 x 882 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 882 is 1
Notice that 1 = HCF(882,1) .
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Frequently Asked Questions on HCF of 560, 977, 882 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, 977, 882?
Answer: HCF of 560, 977, 882 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 977, 882 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 977, 882 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
