Highest Common Factor of 729, 16704 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 729, 16704 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 729, 16704 is 9 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 729, 16704 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 729, 16704 is 9.
HCF(729, 16704) = 9
HCF of 729, 16704 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 729, 16704 is 9.
Highest Common Factor of 729,16704 is 9
Step 1: Since 16704 > 729, we apply the division lemma to 16704 and 729, to get
16704 = 729 x 22 + 666
Step 2: Since the reminder 729 ≠ 0, we apply division lemma to 666 and 729, to get
729 = 666 x 1 + 63
Step 3: We consider the new divisor 666 and the new remainder 63, and apply the division lemma to get
666 = 63 x 10 + 36
We consider the new divisor 63 and the new remainder 36,and apply the division lemma to get
63 = 36 x 1 + 27
We consider the new divisor 36 and the new remainder 27,and apply the division lemma to get
36 = 27 x 1 + 9
We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get
27 = 9 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 729 and 16704 is 9
Notice that 9 = HCF(27,9) = HCF(36,27) = HCF(63,36) = HCF(666,63) = HCF(729,666) = HCF(16704,729) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 729, 16704 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 729, 16704?
Answer: HCF of 729, 16704 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 729, 16704 using Euclid's Algorithm?
Answer: For arbitrary numbers 729, 16704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.