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 470, 3682, 3193 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 470, 3682, 3193 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 470, 3682, 3193 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 470, 3682, 3193 is 1.
HCF(470, 3682, 3193) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 470, 3682, 3193 is 1.
Step 1: Since 3682 > 470, we apply the division lemma to 3682 and 470, to get
3682 = 470 x 7 + 392
Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 392 and 470, to get
470 = 392 x 1 + 78
Step 3: We consider the new divisor 392 and the new remainder 78, and apply the division lemma to get
392 = 78 x 5 + 2
We consider the new divisor 78 and the new remainder 2, and apply the division lemma to get
78 = 2 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 470 and 3682 is 2
Notice that 2 = HCF(78,2) = HCF(392,78) = HCF(470,392) = HCF(3682,470) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3193 > 2, we apply the division lemma to 3193 and 2, to get
3193 = 2 x 1596 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 3193 is 1
Notice that 1 = HCF(2,1) = HCF(3193,2) .
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 470, 3682, 3193?
Answer: HCF of 470, 3682, 3193 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 470, 3682, 3193 using Euclid's Algorithm?
Answer: For arbitrary numbers 470, 3682, 3193 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.