Highest Common Factor of 268, 764, 782, 772 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 268, 764, 782, 772 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 268, 764, 782, 772 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 268, 764, 782, 772 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 268, 764, 782, 772 is 2.
HCF(268, 764, 782, 772) = 2
HCF of 268, 764, 782, 772 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 268, 764, 782, 772 is 2.
Highest Common Factor of 268,764,782,772 is 2
Step 1: Since 764 > 268, we apply the division lemma to 764 and 268, to get
764 = 268 x 2 + 228
Step 2: Since the reminder 268 ≠ 0, we apply division lemma to 228 and 268, to get
268 = 228 x 1 + 40
Step 3: We consider the new divisor 228 and the new remainder 40, and apply the division lemma to get
228 = 40 x 5 + 28
We consider the new divisor 40 and the new remainder 28,and apply the division lemma to get
40 = 28 x 1 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 268 and 764 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(40,28) = HCF(228,40) = HCF(268,228) = HCF(764,268) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 782 > 4, we apply the division lemma to 782 and 4, to get
782 = 4 x 195 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 782 is 2
Notice that 2 = HCF(4,2) = HCF(782,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 772 > 2, we apply the division lemma to 772 and 2, to get
772 = 2 x 386 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 772 is 2
Notice that 2 = HCF(772,2) .
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Frequently Asked Questions on HCF of 268, 764, 782, 772 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 268, 764, 782, 772?
Answer: HCF of 268, 764, 782, 772 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 268, 764, 782, 772 using Euclid's Algorithm?
Answer: For arbitrary numbers 268, 764, 782, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.