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 2748, 7713 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2748, 7713 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 2748, 7713 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 2748, 7713 is 3.
HCF(2748, 7713) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2748, 7713 is 3.
Step 1: Since 7713 > 2748, we apply the division lemma to 7713 and 2748, to get
7713 = 2748 x 2 + 2217
Step 2: Since the reminder 2748 ≠ 0, we apply division lemma to 2217 and 2748, to get
2748 = 2217 x 1 + 531
Step 3: We consider the new divisor 2217 and the new remainder 531, and apply the division lemma to get
2217 = 531 x 4 + 93
We consider the new divisor 531 and the new remainder 93,and apply the division lemma to get
531 = 93 x 5 + 66
We consider the new divisor 93 and the new remainder 66,and apply the division lemma to get
93 = 66 x 1 + 27
We consider the new divisor 66 and the new remainder 27,and apply the division lemma to get
66 = 27 x 2 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2748 and 7713 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(66,27) = HCF(93,66) = HCF(531,93) = HCF(2217,531) = HCF(2748,2217) = HCF(7713,2748) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 2748, 7713?
Answer: HCF of 2748, 7713 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2748, 7713 using Euclid's Algorithm?
Answer: For arbitrary numbers 2748, 7713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.