Highest Common Factor of 675, 7734 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 675, 7734 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 7734 is 3 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 675, 7734 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 675, 7734 is 3.
HCF(675, 7734) = 3
HCF of 675, 7734 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 7734 is 3.
Highest Common Factor of 675,7734 is 3
Step 1: Since 7734 > 675, we apply the division lemma to 7734 and 675, to get
7734 = 675 x 11 + 309
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 309 and 675, to get
675 = 309 x 2 + 57
Step 3: We consider the new divisor 309 and the new remainder 57, and apply the division lemma to get
309 = 57 x 5 + 24
We consider the new divisor 57 and the new remainder 24,and apply the division lemma to get
57 = 24 x 2 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 675 and 7734 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(309,57) = HCF(675,309) = HCF(7734,675) .
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Frequently Asked Questions on HCF of 675, 7734 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 675, 7734?
Answer: HCF of 675, 7734 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 7734 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 7734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.