Highest Common Factor of 6719, 7808, 13742 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 6719, 7808, 13742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6719, 7808, 13742 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 6719, 7808, 13742 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 6719, 7808, 13742 is 1.
HCF(6719, 7808, 13742) = 1
HCF of 6719, 7808, 13742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6719, 7808, 13742 is 1.
Highest Common Factor of 6719,7808,13742 is 1
Step 1: Since 7808 > 6719, we apply the division lemma to 7808 and 6719, to get
7808 = 6719 x 1 + 1089
Step 2: Since the reminder 6719 ≠ 0, we apply division lemma to 1089 and 6719, to get
6719 = 1089 x 6 + 185
Step 3: We consider the new divisor 1089 and the new remainder 185, and apply the division lemma to get
1089 = 185 x 5 + 164
We consider the new divisor 185 and the new remainder 164,and apply the division lemma to get
185 = 164 x 1 + 21
We consider the new divisor 164 and the new remainder 21,and apply the division lemma to get
164 = 21 x 7 + 17
We consider the new divisor 21 and the new remainder 17,and apply the division lemma to get
21 = 17 x 1 + 4
We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get
17 = 4 x 4 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6719 and 7808 is 1
Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(21,17) = HCF(164,21) = HCF(185,164) = HCF(1089,185) = HCF(6719,1089) = HCF(7808,6719) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13742 > 1, we apply the division lemma to 13742 and 1, to get
13742 = 1 x 13742 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 13742 is 1
Notice that 1 = HCF(13742,1) .
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Frequently Asked Questions on HCF of 6719, 7808, 13742 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 6719, 7808, 13742?
Answer: HCF of 6719, 7808, 13742 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6719, 7808, 13742 using Euclid's Algorithm?
Answer: For arbitrary numbers 6719, 7808, 13742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
