Highest Common Factor of 469, 2478 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 469, 2478 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 469, 2478 is 7 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 469, 2478 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 469, 2478 is 7.
HCF(469, 2478) = 7
HCF of 469, 2478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 469, 2478 is 7.
Highest Common Factor of 469,2478 is 7
Step 1: Since 2478 > 469, we apply the division lemma to 2478 and 469, to get
2478 = 469 x 5 + 133
Step 2: Since the reminder 469 ≠ 0, we apply division lemma to 133 and 469, to get
469 = 133 x 3 + 70
Step 3: We consider the new divisor 133 and the new remainder 70, and apply the division lemma to get
133 = 70 x 1 + 63
We consider the new divisor 70 and the new remainder 63,and apply the division lemma to get
70 = 63 x 1 + 7
We consider the new divisor 63 and the new remainder 7,and apply the division lemma to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 469 and 2478 is 7
Notice that 7 = HCF(63,7) = HCF(70,63) = HCF(133,70) = HCF(469,133) = HCF(2478,469) .
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Frequently Asked Questions on HCF of 469, 2478 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 469, 2478?
Answer: HCF of 469, 2478 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 469, 2478 using Euclid's Algorithm?
Answer: For arbitrary numbers 469, 2478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.