Highest Common Factor of 759, 2748 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 759, 2748 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 759, 2748 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 759, 2748 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 759, 2748 is 3.
HCF(759, 2748) = 3
HCF of 759, 2748 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 759, 2748 is 3.
Highest Common Factor of 759,2748 is 3
Step 1: Since 2748 > 759, we apply the division lemma to 2748 and 759, to get
2748 = 759 x 3 + 471
Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 471 and 759, to get
759 = 471 x 1 + 288
Step 3: We consider the new divisor 471 and the new remainder 288, and apply the division lemma to get
471 = 288 x 1 + 183
We consider the new divisor 288 and the new remainder 183,and apply the division lemma to get
288 = 183 x 1 + 105
We consider the new divisor 183 and the new remainder 105,and apply the division lemma to get
183 = 105 x 1 + 78
We consider the new divisor 105 and the new remainder 78,and apply the division lemma to get
105 = 78 x 1 + 27
We consider the new divisor 78 and the new remainder 27,and apply the division lemma to get
78 = 27 x 2 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 759 and 2748 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(78,27) = HCF(105,78) = HCF(183,105) = HCF(288,183) = HCF(471,288) = HCF(759,471) = HCF(2748,759) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 759, 2748 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 759, 2748?
Answer: HCF of 759, 2748 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 759, 2748 using Euclid's Algorithm?
Answer: For arbitrary numbers 759, 2748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.