Highest Common Factor of 738, 8000, 6496 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 738, 8000, 6496 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 8000, 6496 is 2 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 738, 8000, 6496 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 738, 8000, 6496 is 2.
HCF(738, 8000, 6496) = 2
HCF of 738, 8000, 6496 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 738, 8000, 6496 is 2.
Highest Common Factor of 738,8000,6496 is 2
Step 1: Since 8000 > 738, we apply the division lemma to 8000 and 738, to get
8000 = 738 x 10 + 620
Step 2: Since the reminder 738 ≠ 0, we apply division lemma to 620 and 738, to get
738 = 620 x 1 + 118
Step 3: We consider the new divisor 620 and the new remainder 118, and apply the division lemma to get
620 = 118 x 5 + 30
We consider the new divisor 118 and the new remainder 30,and apply the division lemma to get
118 = 30 x 3 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 738 and 8000 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(118,30) = HCF(620,118) = HCF(738,620) = HCF(8000,738) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6496 > 2, we apply the division lemma to 6496 and 2, to get
6496 = 2 x 3248 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 6496 is 2
Notice that 2 = HCF(6496,2) .
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Frequently Asked Questions on HCF of 738, 8000, 6496 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 738, 8000, 6496?
Answer: HCF of 738, 8000, 6496 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 8000, 6496 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 8000, 6496 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.