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, 7964, 57751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2748, 7964, 57751 is 1 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, 7964, 57751 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, 7964, 57751 is 1.
HCF(2748, 7964, 57751) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2748, 7964, 57751 is 1.
Step 1: Since 7964 > 2748, we apply the division lemma to 7964 and 2748, to get
7964 = 2748 x 2 + 2468
Step 2: Since the reminder 2748 ≠ 0, we apply division lemma to 2468 and 2748, to get
2748 = 2468 x 1 + 280
Step 3: We consider the new divisor 2468 and the new remainder 280, and apply the division lemma to get
2468 = 280 x 8 + 228
We consider the new divisor 280 and the new remainder 228,and apply the division lemma to get
280 = 228 x 1 + 52
We consider the new divisor 228 and the new remainder 52,and apply the division lemma to get
228 = 52 x 4 + 20
We consider the new divisor 52 and the new remainder 20,and apply the division lemma to get
52 = 20 x 2 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2748 and 7964 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(52,20) = HCF(228,52) = HCF(280,228) = HCF(2468,280) = HCF(2748,2468) = HCF(7964,2748) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57751 > 4, we apply the division lemma to 57751 and 4, to get
57751 = 4 x 14437 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 57751 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(57751,4) .
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, 7964, 57751?
Answer: HCF of 2748, 7964, 57751 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2748, 7964, 57751 using Euclid's Algorithm?
Answer: For arbitrary numbers 2748, 7964, 57751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.