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 5697, 7728, 69585 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 5697, 7728, 69585 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 5697, 7728, 69585 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 5697, 7728, 69585 is 3.
HCF(5697, 7728, 69585) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5697, 7728, 69585 is 3.
Step 1: Since 7728 > 5697, we apply the division lemma to 7728 and 5697, to get
7728 = 5697 x 1 + 2031
Step 2: Since the reminder 5697 ≠ 0, we apply division lemma to 2031 and 5697, to get
5697 = 2031 x 2 + 1635
Step 3: We consider the new divisor 2031 and the new remainder 1635, and apply the division lemma to get
2031 = 1635 x 1 + 396
We consider the new divisor 1635 and the new remainder 396,and apply the division lemma to get
1635 = 396 x 4 + 51
We consider the new divisor 396 and the new remainder 51,and apply the division lemma to get
396 = 51 x 7 + 39
We consider the new divisor 51 and the new remainder 39,and apply the division lemma to get
51 = 39 x 1 + 12
We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get
39 = 12 x 3 + 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 5697 and 7728 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(396,51) = HCF(1635,396) = HCF(2031,1635) = HCF(5697,2031) = HCF(7728,5697) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69585 > 3, we apply the division lemma to 69585 and 3, to get
69585 = 3 x 23195 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 69585 is 3
Notice that 3 = HCF(69585,3) .
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 5697, 7728, 69585?
Answer: HCF of 5697, 7728, 69585 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5697, 7728, 69585 using Euclid's Algorithm?
Answer: For arbitrary numbers 5697, 7728, 69585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.