Highest Common Factor of 1640, 4536 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 1640, 4536 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 1640, 4536 is 8 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 1640, 4536 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 1640, 4536 is 8.
HCF(1640, 4536) = 8
HCF of 1640, 4536 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1640, 4536 is 8.
Highest Common Factor of 1640,4536 is 8
Step 1: Since 4536 > 1640, we apply the division lemma to 4536 and 1640, to get
4536 = 1640 x 2 + 1256
Step 2: Since the reminder 1640 ≠ 0, we apply division lemma to 1256 and 1640, to get
1640 = 1256 x 1 + 384
Step 3: We consider the new divisor 1256 and the new remainder 384, and apply the division lemma to get
1256 = 384 x 3 + 104
We consider the new divisor 384 and the new remainder 104,and apply the division lemma to get
384 = 104 x 3 + 72
We consider the new divisor 104 and the new remainder 72,and apply the division lemma to get
104 = 72 x 1 + 32
We consider the new divisor 72 and the new remainder 32,and apply the division lemma to get
72 = 32 x 2 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 1640 and 4536 is 8
Notice that 8 = HCF(32,8) = HCF(72,32) = HCF(104,72) = HCF(384,104) = HCF(1256,384) = HCF(1640,1256) = HCF(4536,1640) .
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Frequently Asked Questions on HCF of 1640, 4536 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 1640, 4536?
Answer: HCF of 1640, 4536 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1640, 4536 using Euclid's Algorithm?
Answer: For arbitrary numbers 1640, 4536 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.