Highest Common Factor of 318, 782, 860 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 318, 782, 860 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 318, 782, 860 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 318, 782, 860 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 318, 782, 860 is 2.
HCF(318, 782, 860) = 2
HCF of 318, 782, 860 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 318, 782, 860 is 2.
Highest Common Factor of 318,782,860 is 2
Step 1: Since 782 > 318, we apply the division lemma to 782 and 318, to get
782 = 318 x 2 + 146
Step 2: Since the reminder 318 ≠ 0, we apply division lemma to 146 and 318, to get
318 = 146 x 2 + 26
Step 3: We consider the new divisor 146 and the new remainder 26, and apply the division lemma to get
146 = 26 x 5 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 318 and 782 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(146,26) = HCF(318,146) = HCF(782,318) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 860 > 2, we apply the division lemma to 860 and 2, to get
860 = 2 x 430 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 860 is 2
Notice that 2 = HCF(860,2) .
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Frequently Asked Questions on HCF of 318, 782, 860 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 318, 782, 860?
Answer: HCF of 318, 782, 860 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 318, 782, 860 using Euclid's Algorithm?
Answer: For arbitrary numbers 318, 782, 860 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
