Highest Common Factor of 4536, 4128, 61414 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 4536, 4128, 61414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4536, 4128, 61414 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 4536, 4128, 61414 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 4536, 4128, 61414 is 2.
HCF(4536, 4128, 61414) = 2
HCF of 4536, 4128, 61414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4536, 4128, 61414 is 2.
Highest Common Factor of 4536,4128,61414 is 2
Step 1: Since 4536 > 4128, we apply the division lemma to 4536 and 4128, to get
4536 = 4128 x 1 + 408
Step 2: Since the reminder 4128 ≠ 0, we apply division lemma to 408 and 4128, to get
4128 = 408 x 10 + 48
Step 3: We consider the new divisor 408 and the new remainder 48, and apply the division lemma to get
408 = 48 x 8 + 24
We consider the new divisor 48 and the new remainder 24, and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 4536 and 4128 is 24
Notice that 24 = HCF(48,24) = HCF(408,48) = HCF(4128,408) = HCF(4536,4128) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61414 > 24, we apply the division lemma to 61414 and 24, to get
61414 = 24 x 2558 + 22
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 22 and 24, to get
24 = 22 x 1 + 2
Step 3: We consider the new divisor 22 and the new remainder 2, and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 24 and 61414 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(61414,24) .
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Frequently Asked Questions on HCF of 4536, 4128, 61414 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 4536, 4128, 61414?
Answer: HCF of 4536, 4128, 61414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4536, 4128, 61414 using Euclid's Algorithm?
Answer: For arbitrary numbers 4536, 4128, 61414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.