Highest Common Factor of 2272, 7717 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 2272, 7717 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2272, 7717 is 1 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 2272, 7717 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 2272, 7717 is 1.
HCF(2272, 7717) = 1
HCF of 2272, 7717 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2272, 7717 is 1.
Highest Common Factor of 2272,7717 is 1
Step 1: Since 7717 > 2272, we apply the division lemma to 7717 and 2272, to get
7717 = 2272 x 3 + 901
Step 2: Since the reminder 2272 ≠ 0, we apply division lemma to 901 and 2272, to get
2272 = 901 x 2 + 470
Step 3: We consider the new divisor 901 and the new remainder 470, and apply the division lemma to get
901 = 470 x 1 + 431
We consider the new divisor 470 and the new remainder 431,and apply the division lemma to get
470 = 431 x 1 + 39
We consider the new divisor 431 and the new remainder 39,and apply the division lemma to get
431 = 39 x 11 + 2
We consider the new divisor 39 and the new remainder 2,and apply the division lemma to get
39 = 2 x 19 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2272 and 7717 is 1
Notice that 1 = HCF(2,1) = HCF(39,2) = HCF(431,39) = HCF(470,431) = HCF(901,470) = HCF(2272,901) = HCF(7717,2272) .
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Frequently Asked Questions on HCF of 2272, 7717 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 2272, 7717?
Answer: HCF of 2272, 7717 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2272, 7717 using Euclid's Algorithm?
Answer: For arbitrary numbers 2272, 7717 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.