Highest Common Factor of 2064, 3534 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 2064, 3534 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2064, 3534 is 6 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 2064, 3534 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 2064, 3534 is 6.
HCF(2064, 3534) = 6
HCF of 2064, 3534 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2064, 3534 is 6.
Highest Common Factor of 2064,3534 is 6
Step 1: Since 3534 > 2064, we apply the division lemma to 3534 and 2064, to get
3534 = 2064 x 1 + 1470
Step 2: Since the reminder 2064 ≠ 0, we apply division lemma to 1470 and 2064, to get
2064 = 1470 x 1 + 594
Step 3: We consider the new divisor 1470 and the new remainder 594, and apply the division lemma to get
1470 = 594 x 2 + 282
We consider the new divisor 594 and the new remainder 282,and apply the division lemma to get
594 = 282 x 2 + 30
We consider the new divisor 282 and the new remainder 30,and apply the division lemma to get
282 = 30 x 9 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2064 and 3534 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(282,30) = HCF(594,282) = HCF(1470,594) = HCF(2064,1470) = HCF(3534,2064) .
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Frequently Asked Questions on HCF of 2064, 3534 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 2064, 3534?
Answer: HCF of 2064, 3534 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2064, 3534 using Euclid's Algorithm?
Answer: For arbitrary numbers 2064, 3534 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.