Highest Common Factor of 2417, 9972 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 2417, 9972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2417, 9972 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 2417, 9972 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 2417, 9972 is 1.
HCF(2417, 9972) = 1
HCF of 2417, 9972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2417, 9972 is 1.
Highest Common Factor of 2417,9972 is 1
Step 1: Since 9972 > 2417, we apply the division lemma to 9972 and 2417, to get
9972 = 2417 x 4 + 304
Step 2: Since the reminder 2417 ≠ 0, we apply division lemma to 304 and 2417, to get
2417 = 304 x 7 + 289
Step 3: We consider the new divisor 304 and the new remainder 289, and apply the division lemma to get
304 = 289 x 1 + 15
We consider the new divisor 289 and the new remainder 15,and apply the division lemma to get
289 = 15 x 19 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2417 and 9972 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(289,15) = HCF(304,289) = HCF(2417,304) = HCF(9972,2417) .
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Frequently Asked Questions on HCF of 2417, 9972 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 2417, 9972?
Answer: HCF of 2417, 9972 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2417, 9972 using Euclid's Algorithm?
Answer: For arbitrary numbers 2417, 9972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.