Highest Common Factor of 6924, 8101, 78188 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 6924, 8101, 78188 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6924, 8101, 78188 is 1 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 6924, 8101, 78188 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 6924, 8101, 78188 is 1.
HCF(6924, 8101, 78188) = 1
HCF of 6924, 8101, 78188 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6924, 8101, 78188 is 1.
Highest Common Factor of 6924,8101,78188 is 1
Step 1: Since 8101 > 6924, we apply the division lemma to 8101 and 6924, to get
8101 = 6924 x 1 + 1177
Step 2: Since the reminder 6924 ≠ 0, we apply division lemma to 1177 and 6924, to get
6924 = 1177 x 5 + 1039
Step 3: We consider the new divisor 1177 and the new remainder 1039, and apply the division lemma to get
1177 = 1039 x 1 + 138
We consider the new divisor 1039 and the new remainder 138,and apply the division lemma to get
1039 = 138 x 7 + 73
We consider the new divisor 138 and the new remainder 73,and apply the division lemma to get
138 = 73 x 1 + 65
We consider the new divisor 73 and the new remainder 65,and apply the division lemma to get
73 = 65 x 1 + 8
We consider the new divisor 65 and the new remainder 8,and apply the division lemma to get
65 = 8 x 8 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6924 and 8101 is 1
Notice that 1 = HCF(8,1) = HCF(65,8) = HCF(73,65) = HCF(138,73) = HCF(1039,138) = HCF(1177,1039) = HCF(6924,1177) = HCF(8101,6924) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78188 > 1, we apply the division lemma to 78188 and 1, to get
78188 = 1 x 78188 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78188 is 1
Notice that 1 = HCF(78188,1) .
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Frequently Asked Questions on HCF of 6924, 8101, 78188 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 6924, 8101, 78188?
Answer: HCF of 6924, 8101, 78188 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6924, 8101, 78188 using Euclid's Algorithm?
Answer: For arbitrary numbers 6924, 8101, 78188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.