Highest Common Factor of 7054, 7270 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 7054, 7270 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7054, 7270 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 7054, 7270 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 7054, 7270 is 2.
HCF(7054, 7270) = 2
HCF of 7054, 7270 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7054, 7270 is 2.
Highest Common Factor of 7054,7270 is 2
Step 1: Since 7270 > 7054, we apply the division lemma to 7270 and 7054, to get
7270 = 7054 x 1 + 216
Step 2: Since the reminder 7054 ≠ 0, we apply division lemma to 216 and 7054, to get
7054 = 216 x 32 + 142
Step 3: We consider the new divisor 216 and the new remainder 142, and apply the division lemma to get
216 = 142 x 1 + 74
We consider the new divisor 142 and the new remainder 74,and apply the division lemma to get
142 = 74 x 1 + 68
We consider the new divisor 74 and the new remainder 68,and apply the division lemma to get
74 = 68 x 1 + 6
We consider the new divisor 68 and the new remainder 6,and apply the division lemma to get
68 = 6 x 11 + 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 7054 and 7270 is 2
Notice that 2 = HCF(6,2) = HCF(68,6) = HCF(74,68) = HCF(142,74) = HCF(216,142) = HCF(7054,216) = HCF(7270,7054) .
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Frequently Asked Questions on HCF of 7054, 7270 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 7054, 7270?
Answer: HCF of 7054, 7270 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7054, 7270 using Euclid's Algorithm?
Answer: For arbitrary numbers 7054, 7270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.