Highest Common Factor of 282, 538, 970 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 282, 538, 970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 282, 538, 970 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 282, 538, 970 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 282, 538, 970 is 2.
HCF(282, 538, 970) = 2
HCF of 282, 538, 970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 282, 538, 970 is 2.
Highest Common Factor of 282,538,970 is 2
Step 1: Since 538 > 282, we apply the division lemma to 538 and 282, to get
538 = 282 x 1 + 256
Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 256 and 282, to get
282 = 256 x 1 + 26
Step 3: We consider the new divisor 256 and the new remainder 26, and apply the division lemma to get
256 = 26 x 9 + 22
We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get
26 = 22 x 1 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 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 282 and 538 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(256,26) = HCF(282,256) = HCF(538,282) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 970 > 2, we apply the division lemma to 970 and 2, to get
970 = 2 x 485 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 970 is 2
Notice that 2 = HCF(970,2) .
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Frequently Asked Questions on HCF of 282, 538, 970 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 282, 538, 970?
Answer: HCF of 282, 538, 970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 282, 538, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 282, 538, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.