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 752, 6453, 9864 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 6453, 9864 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 752, 6453, 9864 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 752, 6453, 9864 is 1.
HCF(752, 6453, 9864) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 6453, 9864 is 1.
Step 1: Since 6453 > 752, we apply the division lemma to 6453 and 752, to get
6453 = 752 x 8 + 437
Step 2: Since the reminder 752 ≠ 0, we apply division lemma to 437 and 752, to get
752 = 437 x 1 + 315
Step 3: We consider the new divisor 437 and the new remainder 315, and apply the division lemma to get
437 = 315 x 1 + 122
We consider the new divisor 315 and the new remainder 122,and apply the division lemma to get
315 = 122 x 2 + 71
We consider the new divisor 122 and the new remainder 71,and apply the division lemma to get
122 = 71 x 1 + 51
We consider the new divisor 71 and the new remainder 51,and apply the division lemma to get
71 = 51 x 1 + 20
We consider the new divisor 51 and the new remainder 20,and apply the division lemma to get
51 = 20 x 2 + 11
We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 752 and 6453 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(51,20) = HCF(71,51) = HCF(122,71) = HCF(315,122) = HCF(437,315) = HCF(752,437) = HCF(6453,752) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9864 > 1, we apply the division lemma to 9864 and 1, to get
9864 = 1 x 9864 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9864 is 1
Notice that 1 = HCF(9864,1) .
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 752, 6453, 9864?
Answer: HCF of 752, 6453, 9864 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 6453, 9864 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 6453, 9864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.