Highest Common Factor of 7506, 6754 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 7506, 6754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7506, 6754 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 7506, 6754 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 7506, 6754 is 2.
HCF(7506, 6754) = 2
HCF of 7506, 6754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7506, 6754 is 2.
Highest Common Factor of 7506,6754 is 2
Step 1: Since 7506 > 6754, we apply the division lemma to 7506 and 6754, to get
7506 = 6754 x 1 + 752
Step 2: Since the reminder 6754 ≠ 0, we apply division lemma to 752 and 6754, to get
6754 = 752 x 8 + 738
Step 3: We consider the new divisor 752 and the new remainder 738, and apply the division lemma to get
752 = 738 x 1 + 14
We consider the new divisor 738 and the new remainder 14,and apply the division lemma to get
738 = 14 x 52 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7506 and 6754 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(738,14) = HCF(752,738) = HCF(6754,752) = HCF(7506,6754) .
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Frequently Asked Questions on HCF of 7506, 6754 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 7506, 6754?
Answer: HCF of 7506, 6754 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7506, 6754 using Euclid's Algorithm?
Answer: For arbitrary numbers 7506, 6754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
