Highest Common Factor of 3120, 7530 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 3120, 7530 i.e. 30 the largest integer that leaves a remainder zero for all numbers.
HCF of 3120, 7530 is 30 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 3120, 7530 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 3120, 7530 is 30.
HCF(3120, 7530) = 30
HCF of 3120, 7530 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3120, 7530 is 30.
Highest Common Factor of 3120,7530 is 30
Step 1: Since 7530 > 3120, we apply the division lemma to 7530 and 3120, to get
7530 = 3120 x 2 + 1290
Step 2: Since the reminder 3120 ≠ 0, we apply division lemma to 1290 and 3120, to get
3120 = 1290 x 2 + 540
Step 3: We consider the new divisor 1290 and the new remainder 540, and apply the division lemma to get
1290 = 540 x 2 + 210
We consider the new divisor 540 and the new remainder 210,and apply the division lemma to get
540 = 210 x 2 + 120
We consider the new divisor 210 and the new remainder 120,and apply the division lemma to get
210 = 120 x 1 + 90
We consider the new divisor 120 and the new remainder 90,and apply the division lemma to get
120 = 90 x 1 + 30
We consider the new divisor 90 and the new remainder 30,and apply the division lemma to get
90 = 30 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 3120 and 7530 is 30
Notice that 30 = HCF(90,30) = HCF(120,90) = HCF(210,120) = HCF(540,210) = HCF(1290,540) = HCF(3120,1290) = HCF(7530,3120) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3120, 7530 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 3120, 7530?
Answer: HCF of 3120, 7530 is 30 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3120, 7530 using Euclid's Algorithm?
Answer: For arbitrary numbers 3120, 7530 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.