Highest Common Factor of 6554, 7228 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 6554, 7228 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6554, 7228 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 6554, 7228 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 6554, 7228 is 2.
HCF(6554, 7228) = 2
HCF of 6554, 7228 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6554, 7228 is 2.
Highest Common Factor of 6554,7228 is 2
Step 1: Since 7228 > 6554, we apply the division lemma to 7228 and 6554, to get
7228 = 6554 x 1 + 674
Step 2: Since the reminder 6554 ≠ 0, we apply division lemma to 674 and 6554, to get
6554 = 674 x 9 + 488
Step 3: We consider the new divisor 674 and the new remainder 488, and apply the division lemma to get
674 = 488 x 1 + 186
We consider the new divisor 488 and the new remainder 186,and apply the division lemma to get
488 = 186 x 2 + 116
We consider the new divisor 186 and the new remainder 116,and apply the division lemma to get
186 = 116 x 1 + 70
We consider the new divisor 116 and the new remainder 70,and apply the division lemma to get
116 = 70 x 1 + 46
We consider the new divisor 70 and the new remainder 46,and apply the division lemma to get
70 = 46 x 1 + 24
We consider the new divisor 46 and the new remainder 24,and apply the division lemma to get
46 = 24 x 1 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6554 and 7228 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(46,24) = HCF(70,46) = HCF(116,70) = HCF(186,116) = HCF(488,186) = HCF(674,488) = HCF(6554,674) = HCF(7228,6554) .
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Frequently Asked Questions on HCF of 6554, 7228 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 6554, 7228?
Answer: HCF of 6554, 7228 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6554, 7228 using Euclid's Algorithm?
Answer: For arbitrary numbers 6554, 7228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.