Highest Common Factor of 360, 985, 470 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 360, 985, 470 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 985, 470 is 5 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 360, 985, 470 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 360, 985, 470 is 5.
HCF(360, 985, 470) = 5
HCF of 360, 985, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 985, 470 is 5.
Highest Common Factor of 360,985,470 is 5
Step 1: Since 985 > 360, we apply the division lemma to 985 and 360, to get
985 = 360 x 2 + 265
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 265 and 360, to get
360 = 265 x 1 + 95
Step 3: We consider the new divisor 265 and the new remainder 95, and apply the division lemma to get
265 = 95 x 2 + 75
We consider the new divisor 95 and the new remainder 75,and apply the division lemma to get
95 = 75 x 1 + 20
We consider the new divisor 75 and the new remainder 20,and apply the division lemma to get
75 = 20 x 3 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 360 and 985 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(75,20) = HCF(95,75) = HCF(265,95) = HCF(360,265) = HCF(985,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 5, we apply the division lemma to 470 and 5, to get
470 = 5 x 94 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 470 is 5
Notice that 5 = HCF(470,5) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 360, 985, 470 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 360, 985, 470?
Answer: HCF of 360, 985, 470 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 985, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 985, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.