Highest Common Factor of 3784, 6996 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 3784, 6996 i.e. 44 the largest integer that leaves a remainder zero for all numbers.
HCF of 3784, 6996 is 44 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 3784, 6996 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 3784, 6996 is 44.
HCF(3784, 6996) = 44
HCF of 3784, 6996 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3784, 6996 is 44.
Highest Common Factor of 3784,6996 is 44
Step 1: Since 6996 > 3784, we apply the division lemma to 6996 and 3784, to get
6996 = 3784 x 1 + 3212
Step 2: Since the reminder 3784 ≠ 0, we apply division lemma to 3212 and 3784, to get
3784 = 3212 x 1 + 572
Step 3: We consider the new divisor 3212 and the new remainder 572, and apply the division lemma to get
3212 = 572 x 5 + 352
We consider the new divisor 572 and the new remainder 352,and apply the division lemma to get
572 = 352 x 1 + 220
We consider the new divisor 352 and the new remainder 220,and apply the division lemma to get
352 = 220 x 1 + 132
We consider the new divisor 220 and the new remainder 132,and apply the division lemma to get
220 = 132 x 1 + 88
We consider the new divisor 132 and the new remainder 88,and apply the division lemma to get
132 = 88 x 1 + 44
We consider the new divisor 88 and the new remainder 44,and apply the division lemma to get
88 = 44 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 44, the HCF of 3784 and 6996 is 44
Notice that 44 = HCF(88,44) = HCF(132,88) = HCF(220,132) = HCF(352,220) = HCF(572,352) = HCF(3212,572) = HCF(3784,3212) = HCF(6996,3784) .
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Frequently Asked Questions on HCF of 3784, 6996 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 3784, 6996?
Answer: HCF of 3784, 6996 is 44 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3784, 6996 using Euclid's Algorithm?
Answer: For arbitrary numbers 3784, 6996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.