Highest Common Factor of 8502, 7022 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 8502, 7022 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8502, 7022 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 8502, 7022 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 8502, 7022 is 2.
HCF(8502, 7022) = 2
HCF of 8502, 7022 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8502, 7022 is 2.
Highest Common Factor of 8502,7022 is 2
Step 1: Since 8502 > 7022, we apply the division lemma to 8502 and 7022, to get
8502 = 7022 x 1 + 1480
Step 2: Since the reminder 7022 ≠ 0, we apply division lemma to 1480 and 7022, to get
7022 = 1480 x 4 + 1102
Step 3: We consider the new divisor 1480 and the new remainder 1102, and apply the division lemma to get
1480 = 1102 x 1 + 378
We consider the new divisor 1102 and the new remainder 378,and apply the division lemma to get
1102 = 378 x 2 + 346
We consider the new divisor 378 and the new remainder 346,and apply the division lemma to get
378 = 346 x 1 + 32
We consider the new divisor 346 and the new remainder 32,and apply the division lemma to get
346 = 32 x 10 + 26
We consider the new divisor 32 and the new remainder 26,and apply the division lemma to get
32 = 26 x 1 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8502 and 7022 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(346,32) = HCF(378,346) = HCF(1102,378) = HCF(1480,1102) = HCF(7022,1480) = HCF(8502,7022) .
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Frequently Asked Questions on HCF of 8502, 7022 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 8502, 7022?
Answer: HCF of 8502, 7022 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8502, 7022 using Euclid's Algorithm?
Answer: For arbitrary numbers 8502, 7022 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
