Highest Common Factor of 8702, 7320 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 8702, 7320 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8702, 7320 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 8702, 7320 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 8702, 7320 is 2.
HCF(8702, 7320) = 2
HCF of 8702, 7320 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8702, 7320 is 2.
Highest Common Factor of 8702,7320 is 2
Step 1: Since 8702 > 7320, we apply the division lemma to 8702 and 7320, to get
8702 = 7320 x 1 + 1382
Step 2: Since the reminder 7320 ≠ 0, we apply division lemma to 1382 and 7320, to get
7320 = 1382 x 5 + 410
Step 3: We consider the new divisor 1382 and the new remainder 410, and apply the division lemma to get
1382 = 410 x 3 + 152
We consider the new divisor 410 and the new remainder 152,and apply the division lemma to get
410 = 152 x 2 + 106
We consider the new divisor 152 and the new remainder 106,and apply the division lemma to get
152 = 106 x 1 + 46
We consider the new divisor 106 and the new remainder 46,and apply the division lemma to get
106 = 46 x 2 + 14
We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get
46 = 14 x 3 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8702 and 7320 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(106,46) = HCF(152,106) = HCF(410,152) = HCF(1382,410) = HCF(7320,1382) = HCF(8702,7320) .
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Frequently Asked Questions on HCF of 8702, 7320 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 8702, 7320?
Answer: HCF of 8702, 7320 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8702, 7320 using Euclid's Algorithm?
Answer: For arbitrary numbers 8702, 7320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.