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 785, 405, 906 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 405, 906 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 785, 405, 906 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 785, 405, 906 is 1.
HCF(785, 405, 906) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 405, 906 is 1.
Step 1: Since 785 > 405, we apply the division lemma to 785 and 405, to get
785 = 405 x 1 + 380
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 380 and 405, to get
405 = 380 x 1 + 25
Step 3: We consider the new divisor 380 and the new remainder 25, and apply the division lemma to get
380 = 25 x 15 + 5
We consider the new divisor 25 and the new remainder 5, and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 785 and 405 is 5
Notice that 5 = HCF(25,5) = HCF(380,25) = HCF(405,380) = HCF(785,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 906 > 5, we apply the division lemma to 906 and 5, to get
906 = 5 x 181 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 906 is 1
Notice that 1 = HCF(5,1) = HCF(906,5) .
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 785, 405, 906?
Answer: HCF of 785, 405, 906 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 405, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 405, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.