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 705, 17966 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 17966 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 705, 17966 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 705, 17966 is 1.
HCF(705, 17966) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 17966 is 1.
Step 1: Since 17966 > 705, we apply the division lemma to 17966 and 705, to get
17966 = 705 x 25 + 341
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 341 and 705, to get
705 = 341 x 2 + 23
Step 3: We consider the new divisor 341 and the new remainder 23, and apply the division lemma to get
341 = 23 x 14 + 19
We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get
23 = 19 x 1 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 705 and 17966 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(341,23) = HCF(705,341) = HCF(17966,705) .
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 705, 17966?
Answer: HCF of 705, 17966 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 17966 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 17966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.