Highest Common Factor of 2469, 4374, 53612 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 2469, 4374, 53612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2469, 4374, 53612 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 2469, 4374, 53612 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 2469, 4374, 53612 is 1.
HCF(2469, 4374, 53612) = 1
HCF of 2469, 4374, 53612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2469, 4374, 53612 is 1.
Highest Common Factor of 2469,4374,53612 is 1
Step 1: Since 4374 > 2469, we apply the division lemma to 4374 and 2469, to get
4374 = 2469 x 1 + 1905
Step 2: Since the reminder 2469 ≠ 0, we apply division lemma to 1905 and 2469, to get
2469 = 1905 x 1 + 564
Step 3: We consider the new divisor 1905 and the new remainder 564, and apply the division lemma to get
1905 = 564 x 3 + 213
We consider the new divisor 564 and the new remainder 213,and apply the division lemma to get
564 = 213 x 2 + 138
We consider the new divisor 213 and the new remainder 138,and apply the division lemma to get
213 = 138 x 1 + 75
We consider the new divisor 138 and the new remainder 75,and apply the division lemma to get
138 = 75 x 1 + 63
We consider the new divisor 75 and the new remainder 63,and apply the division lemma to get
75 = 63 x 1 + 12
We consider the new divisor 63 and the new remainder 12,and apply the division lemma to get
63 = 12 x 5 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2469 and 4374 is 3
Notice that 3 = HCF(12,3) = HCF(63,12) = HCF(75,63) = HCF(138,75) = HCF(213,138) = HCF(564,213) = HCF(1905,564) = HCF(2469,1905) = HCF(4374,2469) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 53612 > 3, we apply the division lemma to 53612 and 3, to get
53612 = 3 x 17870 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 53612 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(53612,3) .
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Frequently Asked Questions on HCF of 2469, 4374, 53612 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 2469, 4374, 53612?
Answer: HCF of 2469, 4374, 53612 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2469, 4374, 53612 using Euclid's Algorithm?
Answer: For arbitrary numbers 2469, 4374, 53612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
