Highest Common Factor of 1704, 1406 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 1704, 1406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1704, 1406 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 1704, 1406 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, 1406 is 2.
HCF(1704, 1406) = 2
HCF of 1704, 1406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1704, 1406 is 2.
Highest Common Factor of 1704,1406 is 2
Step 1: Since 1704 > 1406, we apply the division lemma to 1704 and 1406, to get
1704 = 1406 x 1 + 298
Step 2: Since the reminder 1406 ≠ 0, we apply division lemma to 298 and 1406, to get
1406 = 298 x 4 + 214
Step 3: We consider the new divisor 298 and the new remainder 214, and apply the division lemma to get
298 = 214 x 1 + 84
We consider the new divisor 214 and the new remainder 84,and apply the division lemma to get
214 = 84 x 2 + 46
We consider the new divisor 84 and the new remainder 46,and apply the division lemma to get
84 = 46 x 1 + 38
We consider the new divisor 46 and the new remainder 38,and apply the division lemma to get
46 = 38 x 1 + 8
We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get
38 = 8 x 4 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1704 and 1406 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(46,38) = HCF(84,46) = HCF(214,84) = HCF(298,214) = HCF(1406,298) = HCF(1704,1406) .
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Frequently Asked Questions on HCF of 1704, 1406 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 1704, 1406?
Answer: HCF of 1704, 1406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1704, 1406 using Euclid's Algorithm?
Answer: For arbitrary numbers 1704, 1406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.