Highest Common Factor of 710, 470, 170, 324 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 710, 470, 170, 324 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 710, 470, 170, 324 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 710, 470, 170, 324 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 710, 470, 170, 324 is 2.
HCF(710, 470, 170, 324) = 2
HCF of 710, 470, 170, 324 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 710, 470, 170, 324 is 2.
Highest Common Factor of 710,470,170,324 is 2
Step 1: Since 710 > 470, we apply the division lemma to 710 and 470, to get
710 = 470 x 1 + 240
Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 240 and 470, to get
470 = 240 x 1 + 230
Step 3: We consider the new divisor 240 and the new remainder 230, and apply the division lemma to get
240 = 230 x 1 + 10
We consider the new divisor 230 and the new remainder 10, and apply the division lemma to get
230 = 10 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 710 and 470 is 10
Notice that 10 = HCF(230,10) = HCF(240,230) = HCF(470,240) = HCF(710,470) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 170 > 10, we apply the division lemma to 170 and 10, to get
170 = 10 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 170 is 10
Notice that 10 = HCF(170,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 324 > 10, we apply the division lemma to 324 and 10, to get
324 = 10 x 32 + 4
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get
10 = 4 x 2 + 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 10 and 324 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(324,10) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 710, 470, 170, 324 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 710, 470, 170, 324?
Answer: HCF of 710, 470, 170, 324 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 710, 470, 170, 324 using Euclid's Algorithm?
Answer: For arbitrary numbers 710, 470, 170, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.