Highest Common Factor of 997, 10222 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 997, 10222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 997, 10222 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 997, 10222 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 997, 10222 is 1.
HCF(997, 10222) = 1
HCF of 997, 10222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 997, 10222 is 1.
Highest Common Factor of 997,10222 is 1
Step 1: Since 10222 > 997, we apply the division lemma to 10222 and 997, to get
10222 = 997 x 10 + 252
Step 2: Since the reminder 997 ≠ 0, we apply division lemma to 252 and 997, to get
997 = 252 x 3 + 241
Step 3: We consider the new divisor 252 and the new remainder 241, and apply the division lemma to get
252 = 241 x 1 + 11
We consider the new divisor 241 and the new remainder 11,and apply the division lemma to get
241 = 11 x 21 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 997 and 10222 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(241,11) = HCF(252,241) = HCF(997,252) = HCF(10222,997) .
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Frequently Asked Questions on HCF of 997, 10222 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 997, 10222?
Answer: HCF of 997, 10222 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 997, 10222 using Euclid's Algorithm?
Answer: For arbitrary numbers 997, 10222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.