Highest Common Factor of 560, 214 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, 214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 214 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, 214 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, 214 is 2.
HCF(560, 214) = 2
HCF of 560, 214 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, 214 is 2.
Highest Common Factor of 560,214 is 2
Step 1: Since 560 > 214, we apply the division lemma to 560 and 214, to get
560 = 214 x 2 + 132
Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 132 and 214, to get
214 = 132 x 1 + 82
Step 3: We consider the new divisor 132 and the new remainder 82, and apply the division lemma to get
132 = 82 x 1 + 50
We consider the new divisor 82 and the new remainder 50,and apply the division lemma to get
82 = 50 x 1 + 32
We consider the new divisor 50 and the new remainder 32,and apply the division lemma to get
50 = 32 x 1 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 560 and 214 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(50,32) = HCF(82,50) = HCF(132,82) = HCF(214,132) = HCF(560,214) .
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Frequently Asked Questions on HCF of 560, 214 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, 214?
Answer: HCF of 560, 214 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 214 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.