Highest Common Factor of 560, 2006 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, 2006 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 2006 is 2 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, 2006 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, 2006 is 2.
HCF(560, 2006) = 2
HCF of 560, 2006 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, 2006 is 2.
Highest Common Factor of 560,2006 is 2
Step 1: Since 2006 > 560, we apply the division lemma to 2006 and 560, to get
2006 = 560 x 3 + 326
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 326 and 560, to get
560 = 326 x 1 + 234
Step 3: We consider the new divisor 326 and the new remainder 234, and apply the division lemma to get
326 = 234 x 1 + 92
We consider the new divisor 234 and the new remainder 92,and apply the division lemma to get
234 = 92 x 2 + 50
We consider the new divisor 92 and the new remainder 50,and apply the division lemma to get
92 = 50 x 1 + 42
We consider the new divisor 50 and the new remainder 42,and apply the division lemma to get
50 = 42 x 1 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 560 and 2006 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(50,42) = HCF(92,50) = HCF(234,92) = HCF(326,234) = HCF(560,326) = HCF(2006,560) .
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Frequently Asked Questions on HCF of 560, 2006 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, 2006?
Answer: HCF of 560, 2006 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 2006 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 2006 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.