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 728, 894, 160 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 894, 160 is 2 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 728, 894, 160 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 728, 894, 160 is 2.
HCF(728, 894, 160) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 894, 160 is 2.
Step 1: Since 894 > 728, we apply the division lemma to 894 and 728, to get
894 = 728 x 1 + 166
Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 166 and 728, to get
728 = 166 x 4 + 64
Step 3: We consider the new divisor 166 and the new remainder 64, and apply the division lemma to get
166 = 64 x 2 + 38
We consider the new divisor 64 and the new remainder 38,and apply the division lemma to get
64 = 38 x 1 + 26
We consider the new divisor 38 and the new remainder 26,and apply the division lemma to get
38 = 26 x 1 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 728 and 894 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(38,26) = HCF(64,38) = HCF(166,64) = HCF(728,166) = HCF(894,728) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 160 > 2, we apply the division lemma to 160 and 2, to get
160 = 2 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 160 is 2
Notice that 2 = HCF(160,2) .
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 728, 894, 160?
Answer: HCF of 728, 894, 160 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 894, 160 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 894, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.