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 166, 66869 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 166, 66869 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 166, 66869 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 166, 66869 is 1.
HCF(166, 66869) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 166, 66869 is 1.
Step 1: Since 66869 > 166, we apply the division lemma to 66869 and 166, to get
66869 = 166 x 402 + 137
Step 2: Since the reminder 166 ≠ 0, we apply division lemma to 137 and 166, to get
166 = 137 x 1 + 29
Step 3: We consider the new divisor 137 and the new remainder 29, and apply the division lemma to get
137 = 29 x 4 + 21
We consider the new divisor 29 and the new remainder 21,and apply the division lemma to get
29 = 21 x 1 + 8
We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get
21 = 8 x 2 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 166 and 66869 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(29,21) = HCF(137,29) = HCF(166,137) = HCF(66869,166) .
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 166, 66869?
Answer: HCF of 166, 66869 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 166, 66869 using Euclid's Algorithm?
Answer: For arbitrary numbers 166, 66869 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.