Highest Common Factor of 842, 516, 60 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 842, 516, 60 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 842, 516, 60 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 842, 516, 60 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 842, 516, 60 is 2.
HCF(842, 516, 60) = 2
HCF of 842, 516, 60 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 842, 516, 60 is 2.
Highest Common Factor of 842,516,60 is 2
Step 1: Since 842 > 516, we apply the division lemma to 842 and 516, to get
842 = 516 x 1 + 326
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 326 and 516, to get
516 = 326 x 1 + 190
Step 3: We consider the new divisor 326 and the new remainder 190, and apply the division lemma to get
326 = 190 x 1 + 136
We consider the new divisor 190 and the new remainder 136,and apply the division lemma to get
190 = 136 x 1 + 54
We consider the new divisor 136 and the new remainder 54,and apply the division lemma to get
136 = 54 x 2 + 28
We consider the new divisor 54 and the new remainder 28,and apply the division lemma to get
54 = 28 x 1 + 26
We consider the new divisor 28 and the new remainder 26,and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2,and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 842 and 516 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(54,28) = HCF(136,54) = HCF(190,136) = HCF(326,190) = HCF(516,326) = HCF(842,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 2, we apply the division lemma to 60 and 2, to get
60 = 2 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 60 is 2
Notice that 2 = HCF(60,2) .
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Frequently Asked Questions on HCF of 842, 516, 60 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 842, 516, 60?
Answer: HCF of 842, 516, 60 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 842, 516, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 842, 516, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.