Highest Common Factor of 8678, 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 8678, 772 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8678, 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 8678, 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 8678, 772 is 2.
HCF(8678, 772) = 2
HCF of 8678, 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 8678, 772 is 2.
Highest Common Factor of 8678,772 is 2
Step 1: Since 8678 > 772, we apply the division lemma to 8678 and 772, to get
8678 = 772 x 11 + 186
Step 2: Since the reminder 772 ≠ 0, we apply division lemma to 186 and 772, to get
772 = 186 x 4 + 28
Step 3: We consider the new divisor 186 and the new remainder 28, and apply the division lemma to get
186 = 28 x 6 + 18
We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get
28 = 18 x 1 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8678 and 772 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(186,28) = HCF(772,186) = HCF(8678,772) .
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Frequently Asked Questions on HCF of 8678, 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 8678, 772?
Answer: HCF of 8678, 772 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8678, 772 using Euclid's Algorithm?
Answer: For arbitrary numbers 8678, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.