Highest Common Factor of 6750, 4745 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 6750, 4745 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 6750, 4745 is 5 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 6750, 4745 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 6750, 4745 is 5.
HCF(6750, 4745) = 5
HCF of 6750, 4745 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6750, 4745 is 5.
Highest Common Factor of 6750,4745 is 5
Step 1: Since 6750 > 4745, we apply the division lemma to 6750 and 4745, to get
6750 = 4745 x 1 + 2005
Step 2: Since the reminder 4745 ≠ 0, we apply division lemma to 2005 and 4745, to get
4745 = 2005 x 2 + 735
Step 3: We consider the new divisor 2005 and the new remainder 735, and apply the division lemma to get
2005 = 735 x 2 + 535
We consider the new divisor 735 and the new remainder 535,and apply the division lemma to get
735 = 535 x 1 + 200
We consider the new divisor 535 and the new remainder 200,and apply the division lemma to get
535 = 200 x 2 + 135
We consider the new divisor 200 and the new remainder 135,and apply the division lemma to get
200 = 135 x 1 + 65
We consider the new divisor 135 and the new remainder 65,and apply the division lemma to get
135 = 65 x 2 + 5
We consider the new divisor 65 and the new remainder 5,and apply the division lemma to get
65 = 5 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 6750 and 4745 is 5
Notice that 5 = HCF(65,5) = HCF(135,65) = HCF(200,135) = HCF(535,200) = HCF(735,535) = HCF(2005,735) = HCF(4745,2005) = HCF(6750,4745) .
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Frequently Asked Questions on HCF of 6750, 4745 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 6750, 4745?
Answer: HCF of 6750, 4745 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6750, 4745 using Euclid's Algorithm?
Answer: For arbitrary numbers 6750, 4745 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.