Highest Common Factor of 1704, 646 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, 646 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1704, 646 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, 646 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, 646 is 2.
HCF(1704, 646) = 2
HCF of 1704, 646 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, 646 is 2.
Highest Common Factor of 1704,646 is 2
Step 1: Since 1704 > 646, we apply the division lemma to 1704 and 646, to get
1704 = 646 x 2 + 412
Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 412 and 646, to get
646 = 412 x 1 + 234
Step 3: We consider the new divisor 412 and the new remainder 234, and apply the division lemma to get
412 = 234 x 1 + 178
We consider the new divisor 234 and the new remainder 178,and apply the division lemma to get
234 = 178 x 1 + 56
We consider the new divisor 178 and the new remainder 56,and apply the division lemma to get
178 = 56 x 3 + 10
We consider the new divisor 56 and the new remainder 10,and apply the division lemma to get
56 = 10 x 5 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1704 and 646 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(56,10) = HCF(178,56) = HCF(234,178) = HCF(412,234) = HCF(646,412) = HCF(1704,646) .
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Frequently Asked Questions on HCF of 1704, 646 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, 646?
Answer: HCF of 1704, 646 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1704, 646 using Euclid's Algorithm?
Answer: For arbitrary numbers 1704, 646 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.