Highest Common Factor of 6774, 8248 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 6774, 8248 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6774, 8248 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 6774, 8248 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 6774, 8248 is 2.
HCF(6774, 8248) = 2
HCF of 6774, 8248 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6774, 8248 is 2.
Highest Common Factor of 6774,8248 is 2
Step 1: Since 8248 > 6774, we apply the division lemma to 8248 and 6774, to get
8248 = 6774 x 1 + 1474
Step 2: Since the reminder 6774 ≠ 0, we apply division lemma to 1474 and 6774, to get
6774 = 1474 x 4 + 878
Step 3: We consider the new divisor 1474 and the new remainder 878, and apply the division lemma to get
1474 = 878 x 1 + 596
We consider the new divisor 878 and the new remainder 596,and apply the division lemma to get
878 = 596 x 1 + 282
We consider the new divisor 596 and the new remainder 282,and apply the division lemma to get
596 = 282 x 2 + 32
We consider the new divisor 282 and the new remainder 32,and apply the division lemma to get
282 = 32 x 8 + 26
We consider the new divisor 32 and the new remainder 26,and apply the division lemma to get
32 = 26 x 1 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6774 and 8248 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(282,32) = HCF(596,282) = HCF(878,596) = HCF(1474,878) = HCF(6774,1474) = HCF(8248,6774) .
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Frequently Asked Questions on HCF of 6774, 8248 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 6774, 8248?
Answer: HCF of 6774, 8248 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6774, 8248 using Euclid's Algorithm?
Answer: For arbitrary numbers 6774, 8248 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.