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 746, 411, 864 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 411, 864 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 746, 411, 864 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 746, 411, 864 is 1.
HCF(746, 411, 864) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 411, 864 is 1.
Step 1: Since 746 > 411, we apply the division lemma to 746 and 411, to get
746 = 411 x 1 + 335
Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 335 and 411, to get
411 = 335 x 1 + 76
Step 3: We consider the new divisor 335 and the new remainder 76, and apply the division lemma to get
335 = 76 x 4 + 31
We consider the new divisor 76 and the new remainder 31,and apply the division lemma to get
76 = 31 x 2 + 14
We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get
31 = 14 x 2 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 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 746 and 411 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(76,31) = HCF(335,76) = HCF(411,335) = HCF(746,411) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 864 > 1, we apply the division lemma to 864 and 1, to get
864 = 1 x 864 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 864 is 1
Notice that 1 = HCF(864,1) .
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 746, 411, 864?
Answer: HCF of 746, 411, 864 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 411, 864 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 411, 864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.