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 406, 699, 164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 406, 699, 164 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 406, 699, 164 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 406, 699, 164 is 1.
HCF(406, 699, 164) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 406, 699, 164 is 1.
Step 1: Since 699 > 406, we apply the division lemma to 699 and 406, to get
699 = 406 x 1 + 293
Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 293 and 406, to get
406 = 293 x 1 + 113
Step 3: We consider the new divisor 293 and the new remainder 113, and apply the division lemma to get
293 = 113 x 2 + 67
We consider the new divisor 113 and the new remainder 67,and apply the division lemma to get
113 = 67 x 1 + 46
We consider the new divisor 67 and the new remainder 46,and apply the division lemma to get
67 = 46 x 1 + 21
We consider the new divisor 46 and the new remainder 21,and apply the division lemma to get
46 = 21 x 2 + 4
We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get
21 = 4 x 5 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 406 and 699 is 1
Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(46,21) = HCF(67,46) = HCF(113,67) = HCF(293,113) = HCF(406,293) = HCF(699,406) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 164 > 1, we apply the division lemma to 164 and 1, to get
164 = 1 x 164 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 164 is 1
Notice that 1 = HCF(164,1) .
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 406, 699, 164?
Answer: HCF of 406, 699, 164 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 406, 699, 164 using Euclid's Algorithm?
Answer: For arbitrary numbers 406, 699, 164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.