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 585, 2470, 4672 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 585, 2470, 4672 is 1 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 585, 2470, 4672 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 585, 2470, 4672 is 1.
HCF(585, 2470, 4672) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 585, 2470, 4672 is 1.
Step 1: Since 2470 > 585, we apply the division lemma to 2470 and 585, to get
2470 = 585 x 4 + 130
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 130 and 585, to get
585 = 130 x 4 + 65
Step 3: We consider the new divisor 130 and the new remainder 65, and apply the division lemma to get
130 = 65 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 585 and 2470 is 65
Notice that 65 = HCF(130,65) = HCF(585,130) = HCF(2470,585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4672 > 65, we apply the division lemma to 4672 and 65, to get
4672 = 65 x 71 + 57
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 57 and 65, to get
65 = 57 x 1 + 8
Step 3: We consider the new divisor 57 and the new remainder 8, and apply the division lemma to get
57 = 8 x 7 + 1
We consider the new divisor 8 and the new remainder 1, and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 65 and 4672 is 1
Notice that 1 = HCF(8,1) = HCF(57,8) = HCF(65,57) = HCF(4672,65) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 585, 2470, 4672?
Answer: HCF of 585, 2470, 4672 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 585, 2470, 4672 using Euclid's Algorithm?
Answer: For arbitrary numbers 585, 2470, 4672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.