Highest Common Factor of 560, 210, 282 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, 210, 282 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 210, 282 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, 210, 282 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, 210, 282 is 2.
HCF(560, 210, 282) = 2
HCF of 560, 210, 282 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, 210, 282 is 2.
Highest Common Factor of 560,210,282 is 2
Step 1: Since 560 > 210, we apply the division lemma to 560 and 210, to get
560 = 210 x 2 + 140
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 140 and 210, to get
210 = 140 x 1 + 70
Step 3: We consider the new divisor 140 and the new remainder 70, and apply the division lemma to get
140 = 70 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 70, the HCF of 560 and 210 is 70
Notice that 70 = HCF(140,70) = HCF(210,140) = HCF(560,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 282 > 70, we apply the division lemma to 282 and 70, to get
282 = 70 x 4 + 2
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 2 and 70, to get
70 = 2 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 70 and 282 is 2
Notice that 2 = HCF(70,2) = HCF(282,70) .
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Frequently Asked Questions on HCF of 560, 210, 282 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, 210, 282?
Answer: HCF of 560, 210, 282 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 210, 282 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 210, 282 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.