Highest Common Factor of 2219, 9702 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 2219, 9702 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 2219, 9702 is 7 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 2219, 9702 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 2219, 9702 is 7.
HCF(2219, 9702) = 7
HCF of 2219, 9702 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2219, 9702 is 7.
Highest Common Factor of 2219,9702 is 7
Step 1: Since 9702 > 2219, we apply the division lemma to 9702 and 2219, to get
9702 = 2219 x 4 + 826
Step 2: Since the reminder 2219 ≠ 0, we apply division lemma to 826 and 2219, to get
2219 = 826 x 2 + 567
Step 3: We consider the new divisor 826 and the new remainder 567, and apply the division lemma to get
826 = 567 x 1 + 259
We consider the new divisor 567 and the new remainder 259,and apply the division lemma to get
567 = 259 x 2 + 49
We consider the new divisor 259 and the new remainder 49,and apply the division lemma to get
259 = 49 x 5 + 14
We consider the new divisor 49 and the new remainder 14,and apply the division lemma to get
49 = 14 x 3 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 2219 and 9702 is 7
Notice that 7 = HCF(14,7) = HCF(49,14) = HCF(259,49) = HCF(567,259) = HCF(826,567) = HCF(2219,826) = HCF(9702,2219) .
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Frequently Asked Questions on HCF of 2219, 9702 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 2219, 9702?
Answer: HCF of 2219, 9702 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2219, 9702 using Euclid's Algorithm?
Answer: For arbitrary numbers 2219, 9702 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.