Highest Common Factor of 728, 988, 894 using Euclid's algorithm
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, 988, 894 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 988, 894 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, 988, 894 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, 988, 894 is 2.
HCF(728, 988, 894) = 2
HCF of 728, 988, 894 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 988, 894 is 2.
Highest Common Factor of 728,988,894 is 2
Step 1: Since 988 > 728, we apply the division lemma to 988 and 728, to get
988 = 728 x 1 + 260
Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 260 and 728, to get
728 = 260 x 2 + 208
Step 3: We consider the new divisor 260 and the new remainder 208, and apply the division lemma to get
260 = 208 x 1 + 52
We consider the new divisor 208 and the new remainder 52, and apply the division lemma to get
208 = 52 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 728 and 988 is 52
Notice that 52 = HCF(208,52) = HCF(260,208) = HCF(728,260) = HCF(988,728) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 894 > 52, we apply the division lemma to 894 and 52, to get
894 = 52 x 17 + 10
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 10 and 52, to get
52 = 10 x 5 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 52 and 894 is 2
Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(894,52) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 728, 988, 894 using Euclid's Algorithm
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, 988, 894?
Answer: HCF of 728, 988, 894 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 988, 894 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 988, 894 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.