Highest Common Factor of 7878, 6812 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 7878, 6812 i.e. 26 the largest integer that leaves a remainder zero for all numbers.
HCF of 7878, 6812 is 26 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 7878, 6812 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 7878, 6812 is 26.
HCF(7878, 6812) = 26
HCF of 7878, 6812 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7878, 6812 is 26.
Highest Common Factor of 7878,6812 is 26
Step 1: Since 7878 > 6812, we apply the division lemma to 7878 and 6812, to get
7878 = 6812 x 1 + 1066
Step 2: Since the reminder 6812 ≠ 0, we apply division lemma to 1066 and 6812, to get
6812 = 1066 x 6 + 416
Step 3: We consider the new divisor 1066 and the new remainder 416, and apply the division lemma to get
1066 = 416 x 2 + 234
We consider the new divisor 416 and the new remainder 234,and apply the division lemma to get
416 = 234 x 1 + 182
We consider the new divisor 234 and the new remainder 182,and apply the division lemma to get
234 = 182 x 1 + 52
We consider the new divisor 182 and the new remainder 52,and apply the division lemma to get
182 = 52 x 3 + 26
We consider the new divisor 52 and the new remainder 26,and apply the division lemma to get
52 = 26 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 7878 and 6812 is 26
Notice that 26 = HCF(52,26) = HCF(182,52) = HCF(234,182) = HCF(416,234) = HCF(1066,416) = HCF(6812,1066) = HCF(7878,6812) .
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Frequently Asked Questions on HCF of 7878, 6812 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 7878, 6812?
Answer: HCF of 7878, 6812 is 26 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7878, 6812 using Euclid's Algorithm?
Answer: For arbitrary numbers 7878, 6812 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.