Highest Common Factor of 878, 77808 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 878, 77808 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 878, 77808 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 878, 77808 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 878, 77808 is 2.
HCF(878, 77808) = 2
HCF of 878, 77808 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 878, 77808 is 2.
Highest Common Factor of 878,77808 is 2
Step 1: Since 77808 > 878, we apply the division lemma to 77808 and 878, to get
77808 = 878 x 88 + 544
Step 2: Since the reminder 878 ≠ 0, we apply division lemma to 544 and 878, to get
878 = 544 x 1 + 334
Step 3: We consider the new divisor 544 and the new remainder 334, and apply the division lemma to get
544 = 334 x 1 + 210
We consider the new divisor 334 and the new remainder 210,and apply the division lemma to get
334 = 210 x 1 + 124
We consider the new divisor 210 and the new remainder 124,and apply the division lemma to get
210 = 124 x 1 + 86
We consider the new divisor 124 and the new remainder 86,and apply the division lemma to get
124 = 86 x 1 + 38
We consider the new divisor 86 and the new remainder 38,and apply the division lemma to get
86 = 38 x 2 + 10
We consider the new divisor 38 and the new remainder 10,and apply the division lemma to get
38 = 10 x 3 + 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 878 and 77808 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(38,10) = HCF(86,38) = HCF(124,86) = HCF(210,124) = HCF(334,210) = HCF(544,334) = HCF(878,544) = HCF(77808,878) .
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Frequently Asked Questions on HCF of 878, 77808 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 878, 77808?
Answer: HCF of 878, 77808 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 878, 77808 using Euclid's Algorithm?
Answer: For arbitrary numbers 878, 77808 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
