Highest Common Factor of 210, 963, 560 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 210, 963, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 963, 560 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 210, 963, 560 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 210, 963, 560 is 1.
HCF(210, 963, 560) = 1
HCF of 210, 963, 560 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 963, 560 is 1.
Highest Common Factor of 210,963,560 is 1
Step 1: Since 963 > 210, we apply the division lemma to 963 and 210, to get
963 = 210 x 4 + 123
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 123 and 210, to get
210 = 123 x 1 + 87
Step 3: We consider the new divisor 123 and the new remainder 87, and apply the division lemma to get
123 = 87 x 1 + 36
We consider the new divisor 87 and the new remainder 36,and apply the division lemma to get
87 = 36 x 2 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 210 and 963 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(87,36) = HCF(123,87) = HCF(210,123) = HCF(963,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 560 > 3, we apply the division lemma to 560 and 3, to get
560 = 3 x 186 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 560 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(560,3) .
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Frequently Asked Questions on HCF of 210, 963, 560 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 210, 963, 560?
Answer: HCF of 210, 963, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 963, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 963, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.