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 1530, 4072, 68070 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1530, 4072, 68070 is 2 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 1530, 4072, 68070 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 1530, 4072, 68070 is 2.
HCF(1530, 4072, 68070) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1530, 4072, 68070 is 2.
Step 1: Since 4072 > 1530, we apply the division lemma to 4072 and 1530, to get
4072 = 1530 x 2 + 1012
Step 2: Since the reminder 1530 ≠ 0, we apply division lemma to 1012 and 1530, to get
1530 = 1012 x 1 + 518
Step 3: We consider the new divisor 1012 and the new remainder 518, and apply the division lemma to get
1012 = 518 x 1 + 494
We consider the new divisor 518 and the new remainder 494,and apply the division lemma to get
518 = 494 x 1 + 24
We consider the new divisor 494 and the new remainder 24,and apply the division lemma to get
494 = 24 x 20 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1530 and 4072 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(494,24) = HCF(518,494) = HCF(1012,518) = HCF(1530,1012) = HCF(4072,1530) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68070 > 2, we apply the division lemma to 68070 and 2, to get
68070 = 2 x 34035 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 68070 is 2
Notice that 2 = HCF(68070,2) .
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 1530, 4072, 68070?
Answer: HCF of 1530, 4072, 68070 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1530, 4072, 68070 using Euclid's Algorithm?
Answer: For arbitrary numbers 1530, 4072, 68070 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.