Highest Common Factor of 7576, 8222 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 7576, 8222 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7576, 8222 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 7576, 8222 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 7576, 8222 is 2.
HCF(7576, 8222) = 2
HCF of 7576, 8222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7576, 8222 is 2.
Highest Common Factor of 7576,8222 is 2
Step 1: Since 8222 > 7576, we apply the division lemma to 8222 and 7576, to get
8222 = 7576 x 1 + 646
Step 2: Since the reminder 7576 ≠ 0, we apply division lemma to 646 and 7576, to get
7576 = 646 x 11 + 470
Step 3: We consider the new divisor 646 and the new remainder 470, and apply the division lemma to get
646 = 470 x 1 + 176
We consider the new divisor 470 and the new remainder 176,and apply the division lemma to get
470 = 176 x 2 + 118
We consider the new divisor 176 and the new remainder 118,and apply the division lemma to get
176 = 118 x 1 + 58
We consider the new divisor 118 and the new remainder 58,and apply the division lemma to get
118 = 58 x 2 + 2
We consider the new divisor 58 and the new remainder 2,and apply the division lemma to get
58 = 2 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7576 and 8222 is 2
Notice that 2 = HCF(58,2) = HCF(118,58) = HCF(176,118) = HCF(470,176) = HCF(646,470) = HCF(7576,646) = HCF(8222,7576) .
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Frequently Asked Questions on HCF of 7576, 8222 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 7576, 8222?
Answer: HCF of 7576, 8222 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7576, 8222 using Euclid's Algorithm?
Answer: For arbitrary numbers 7576, 8222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.