Highest Common Factor of 3750, 7104 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 3750, 7104 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 3750, 7104 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 3750, 7104 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 3750, 7104 is 6.
HCF(3750, 7104) = 6
HCF of 3750, 7104 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3750, 7104 is 6.
Highest Common Factor of 3750,7104 is 6
Step 1: Since 7104 > 3750, we apply the division lemma to 7104 and 3750, to get
7104 = 3750 x 1 + 3354
Step 2: Since the reminder 3750 ≠ 0, we apply division lemma to 3354 and 3750, to get
3750 = 3354 x 1 + 396
Step 3: We consider the new divisor 3354 and the new remainder 396, and apply the division lemma to get
3354 = 396 x 8 + 186
We consider the new divisor 396 and the new remainder 186,and apply the division lemma to get
396 = 186 x 2 + 24
We consider the new divisor 186 and the new remainder 24,and apply the division lemma to get
186 = 24 x 7 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 3750 and 7104 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(186,24) = HCF(396,186) = HCF(3354,396) = HCF(3750,3354) = HCF(7104,3750) .
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Frequently Asked Questions on HCF of 3750, 7104 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 3750, 7104?
Answer: HCF of 3750, 7104 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3750, 7104 using Euclid's Algorithm?
Answer: For arbitrary numbers 3750, 7104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
