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 1704, 6687 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1704, 6687 is 3 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 1704, 6687 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 1704, 6687 is 3.
HCF(1704, 6687) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1704, 6687 is 3.
Step 1: Since 6687 > 1704, we apply the division lemma to 6687 and 1704, to get
6687 = 1704 x 3 + 1575
Step 2: Since the reminder 1704 ≠ 0, we apply division lemma to 1575 and 1704, to get
1704 = 1575 x 1 + 129
Step 3: We consider the new divisor 1575 and the new remainder 129, and apply the division lemma to get
1575 = 129 x 12 + 27
We consider the new divisor 129 and the new remainder 27,and apply the division lemma to get
129 = 27 x 4 + 21
We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get
27 = 21 x 1 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1704 and 6687 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(129,27) = HCF(1575,129) = HCF(1704,1575) = HCF(6687,1704) .
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 1704, 6687?
Answer: HCF of 1704, 6687 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1704, 6687 using Euclid's Algorithm?
Answer: For arbitrary numbers 1704, 6687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.