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 441, 728 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 441, 728 is 7 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 441, 728 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 441, 728 is 7.
HCF(441, 728) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 441, 728 is 7.
Step 1: Since 728 > 441, we apply the division lemma to 728 and 441, to get
728 = 441 x 1 + 287
Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 287 and 441, to get
441 = 287 x 1 + 154
Step 3: We consider the new divisor 287 and the new remainder 154, and apply the division lemma to get
287 = 154 x 1 + 133
We consider the new divisor 154 and the new remainder 133,and apply the division lemma to get
154 = 133 x 1 + 21
We consider the new divisor 133 and the new remainder 21,and apply the division lemma to get
133 = 21 x 6 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 441 and 728 is 7
Notice that 7 = HCF(21,7) = HCF(133,21) = HCF(154,133) = HCF(287,154) = HCF(441,287) = HCF(728,441) .
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 441, 728?
Answer: HCF of 441, 728 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 441, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 441, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.