Highest Common Factor of 2036, 3204 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 2036, 3204 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2036, 3204 is 4 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 2036, 3204 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 2036, 3204 is 4.
HCF(2036, 3204) = 4
HCF of 2036, 3204 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2036, 3204 is 4.
Highest Common Factor of 2036,3204 is 4
Step 1: Since 3204 > 2036, we apply the division lemma to 3204 and 2036, to get
3204 = 2036 x 1 + 1168
Step 2: Since the reminder 2036 ≠ 0, we apply division lemma to 1168 and 2036, to get
2036 = 1168 x 1 + 868
Step 3: We consider the new divisor 1168 and the new remainder 868, and apply the division lemma to get
1168 = 868 x 1 + 300
We consider the new divisor 868 and the new remainder 300,and apply the division lemma to get
868 = 300 x 2 + 268
We consider the new divisor 300 and the new remainder 268,and apply the division lemma to get
300 = 268 x 1 + 32
We consider the new divisor 268 and the new remainder 32,and apply the division lemma to get
268 = 32 x 8 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2036 and 3204 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(268,32) = HCF(300,268) = HCF(868,300) = HCF(1168,868) = HCF(2036,1168) = HCF(3204,2036) .
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Frequently Asked Questions on HCF of 2036, 3204 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 2036, 3204?
Answer: HCF of 2036, 3204 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2036, 3204 using Euclid's Algorithm?
Answer: For arbitrary numbers 2036, 3204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.