Highest Common Factor of 480, 810, 670 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 480, 810, 670 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 480, 810, 670 is 10 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 480, 810, 670 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 480, 810, 670 is 10.
HCF(480, 810, 670) = 10
HCF of 480, 810, 670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 480, 810, 670 is 10.
Highest Common Factor of 480,810,670 is 10
Step 1: Since 810 > 480, we apply the division lemma to 810 and 480, to get
810 = 480 x 1 + 330
Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 330 and 480, to get
480 = 330 x 1 + 150
Step 3: We consider the new divisor 330 and the new remainder 150, and apply the division lemma to get
330 = 150 x 2 + 30
We consider the new divisor 150 and the new remainder 30, and apply the division lemma to get
150 = 30 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 480 and 810 is 30
Notice that 30 = HCF(150,30) = HCF(330,150) = HCF(480,330) = HCF(810,480) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 670 > 30, we apply the division lemma to 670 and 30, to get
670 = 30 x 22 + 10
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 10 and 30, to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 30 and 670 is 10
Notice that 10 = HCF(30,10) = HCF(670,30) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 480, 810, 670 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 480, 810, 670?
Answer: HCF of 480, 810, 670 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 480, 810, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 480, 810, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.