Highest Common Factor of 7766, 8780 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 7766, 8780 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7766, 8780 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 7766, 8780 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 7766, 8780 is 2.
HCF(7766, 8780) = 2
HCF of 7766, 8780 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7766, 8780 is 2.
Highest Common Factor of 7766,8780 is 2
Step 1: Since 8780 > 7766, we apply the division lemma to 8780 and 7766, to get
8780 = 7766 x 1 + 1014
Step 2: Since the reminder 7766 ≠ 0, we apply division lemma to 1014 and 7766, to get
7766 = 1014 x 7 + 668
Step 3: We consider the new divisor 1014 and the new remainder 668, and apply the division lemma to get
1014 = 668 x 1 + 346
We consider the new divisor 668 and the new remainder 346,and apply the division lemma to get
668 = 346 x 1 + 322
We consider the new divisor 346 and the new remainder 322,and apply the division lemma to get
346 = 322 x 1 + 24
We consider the new divisor 322 and the new remainder 24,and apply the division lemma to get
322 = 24 x 13 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 7766 and 8780 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(322,24) = HCF(346,322) = HCF(668,346) = HCF(1014,668) = HCF(7766,1014) = HCF(8780,7766) .
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Frequently Asked Questions on HCF of 7766, 8780 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 7766, 8780?
Answer: HCF of 7766, 8780 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7766, 8780 using Euclid's Algorithm?
Answer: For arbitrary numbers 7766, 8780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.