Highest Common Factor of 7119, 2109 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 7119, 2109 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 7119, 2109 is 3 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 7119, 2109 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 7119, 2109 is 3.
HCF(7119, 2109) = 3
HCF of 7119, 2109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7119, 2109 is 3.
Highest Common Factor of 7119,2109 is 3
Step 1: Since 7119 > 2109, we apply the division lemma to 7119 and 2109, to get
7119 = 2109 x 3 + 792
Step 2: Since the reminder 2109 ≠ 0, we apply division lemma to 792 and 2109, to get
2109 = 792 x 2 + 525
Step 3: We consider the new divisor 792 and the new remainder 525, and apply the division lemma to get
792 = 525 x 1 + 267
We consider the new divisor 525 and the new remainder 267,and apply the division lemma to get
525 = 267 x 1 + 258
We consider the new divisor 267 and the new remainder 258,and apply the division lemma to get
267 = 258 x 1 + 9
We consider the new divisor 258 and the new remainder 9,and apply the division lemma to get
258 = 9 x 28 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7119 and 2109 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(258,9) = HCF(267,258) = HCF(525,267) = HCF(792,525) = HCF(2109,792) = HCF(7119,2109) .
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Frequently Asked Questions on HCF of 7119, 2109 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 7119, 2109?
Answer: HCF of 7119, 2109 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7119, 2109 using Euclid's Algorithm?
Answer: For arbitrary numbers 7119, 2109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.