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 868, 566, 401 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 868, 566, 401 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 868, 566, 401 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 868, 566, 401 is 1.
HCF(868, 566, 401) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 868, 566, 401 is 1.
Step 1: Since 868 > 566, we apply the division lemma to 868 and 566, to get
868 = 566 x 1 + 302
Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 302 and 566, to get
566 = 302 x 1 + 264
Step 3: We consider the new divisor 302 and the new remainder 264, and apply the division lemma to get
302 = 264 x 1 + 38
We consider the new divisor 264 and the new remainder 38,and apply the division lemma to get
264 = 38 x 6 + 36
We consider the new divisor 38 and the new remainder 36,and apply the division lemma to get
38 = 36 x 1 + 2
We consider the new divisor 36 and the new remainder 2,and apply the division lemma to get
36 = 2 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 868 and 566 is 2
Notice that 2 = HCF(36,2) = HCF(38,36) = HCF(264,38) = HCF(302,264) = HCF(566,302) = HCF(868,566) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 401 > 2, we apply the division lemma to 401 and 2, to get
401 = 2 x 200 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 401 is 1
Notice that 1 = HCF(2,1) = HCF(401,2) .
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 868, 566, 401?
Answer: HCF of 868, 566, 401 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 868, 566, 401 using Euclid's Algorithm?
Answer: For arbitrary numbers 868, 566, 401 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.