Highest Common Factor of 738, 930, 580 using Euclid's algorithm
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 738, 930, 580 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 930, 580 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 738, 930, 580 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 738, 930, 580 is 2.
HCF(738, 930, 580) = 2
HCF of 738, 930, 580 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 738, 930, 580 is 2.
Highest Common Factor of 738,930,580 is 2
Step 1: Since 930 > 738, we apply the division lemma to 930 and 738, to get
930 = 738 x 1 + 192
Step 2: Since the reminder 738 ≠ 0, we apply division lemma to 192 and 738, to get
738 = 192 x 3 + 162
Step 3: We consider the new divisor 192 and the new remainder 162, and apply the division lemma to get
192 = 162 x 1 + 30
We consider the new divisor 162 and the new remainder 30,and apply the division lemma to get
162 = 30 x 5 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 738 and 930 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(162,30) = HCF(192,162) = HCF(738,192) = HCF(930,738) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 580 > 6, we apply the division lemma to 580 and 6, to get
580 = 6 x 96 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 580 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(580,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 738, 930, 580 using Euclid's Algorithm
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 738, 930, 580?
Answer: HCF of 738, 930, 580 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 930, 580 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 930, 580 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.