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 9719, 7424, 57642 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9719, 7424, 57642 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 9719, 7424, 57642 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 9719, 7424, 57642 is 1.
HCF(9719, 7424, 57642) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9719, 7424, 57642 is 1.
Step 1: Since 9719 > 7424, we apply the division lemma to 9719 and 7424, to get
9719 = 7424 x 1 + 2295
Step 2: Since the reminder 7424 ≠ 0, we apply division lemma to 2295 and 7424, to get
7424 = 2295 x 3 + 539
Step 3: We consider the new divisor 2295 and the new remainder 539, and apply the division lemma to get
2295 = 539 x 4 + 139
We consider the new divisor 539 and the new remainder 139,and apply the division lemma to get
539 = 139 x 3 + 122
We consider the new divisor 139 and the new remainder 122,and apply the division lemma to get
139 = 122 x 1 + 17
We consider the new divisor 122 and the new remainder 17,and apply the division lemma to get
122 = 17 x 7 + 3
We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get
17 = 3 x 5 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 9719 and 7424 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(122,17) = HCF(139,122) = HCF(539,139) = HCF(2295,539) = HCF(7424,2295) = HCF(9719,7424) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57642 > 1, we apply the division lemma to 57642 and 1, to get
57642 = 1 x 57642 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57642 is 1
Notice that 1 = HCF(57642,1) .
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 9719, 7424, 57642?
Answer: HCF of 9719, 7424, 57642 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9719, 7424, 57642 using Euclid's Algorithm?
Answer: For arbitrary numbers 9719, 7424, 57642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.