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, 578 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 578 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, 578 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, 578 is 1.
HCF(785, 578) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 578 is 1.
Step 1: Since 785 > 578, we apply the division lemma to 785 and 578, to get
785 = 578 x 1 + 207
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 207 and 578, to get
578 = 207 x 2 + 164
Step 3: We consider the new divisor 207 and the new remainder 164, and apply the division lemma to get
207 = 164 x 1 + 43
We consider the new divisor 164 and the new remainder 43,and apply the division lemma to get
164 = 43 x 3 + 35
We consider the new divisor 43 and the new remainder 35,and apply the division lemma to get
43 = 35 x 1 + 8
We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get
35 = 8 x 4 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 785 and 578 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(43,35) = HCF(164,43) = HCF(207,164) = HCF(578,207) = HCF(785,578) .
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, 578?
Answer: HCF of 785, 578 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.