Highest Common Factor of 902, 8702 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 902, 8702 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 8702 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 902, 8702 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 902, 8702 is 2.
HCF(902, 8702) = 2
HCF of 902, 8702 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 902, 8702 is 2.
Highest Common Factor of 902,8702 is 2
Step 1: Since 8702 > 902, we apply the division lemma to 8702 and 902, to get
8702 = 902 x 9 + 584
Step 2: Since the reminder 902 ≠ 0, we apply division lemma to 584 and 902, to get
902 = 584 x 1 + 318
Step 3: We consider the new divisor 584 and the new remainder 318, and apply the division lemma to get
584 = 318 x 1 + 266
We consider the new divisor 318 and the new remainder 266,and apply the division lemma to get
318 = 266 x 1 + 52
We consider the new divisor 266 and the new remainder 52,and apply the division lemma to get
266 = 52 x 5 + 6
We consider the new divisor 52 and the new remainder 6,and apply the division lemma to get
52 = 6 x 8 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 902 and 8702 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(52,6) = HCF(266,52) = HCF(318,266) = HCF(584,318) = HCF(902,584) = HCF(8702,902) .
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Frequently Asked Questions on HCF of 902, 8702 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 902, 8702?
Answer: HCF of 902, 8702 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 8702 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 8702 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.