Highest Common Factor of 1704, 7538 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, 7538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1704, 7538 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, 7538 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, 7538 is 2.
HCF(1704, 7538) = 2
HCF of 1704, 7538 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, 7538 is 2.
Highest Common Factor of 1704,7538 is 2
Step 1: Since 7538 > 1704, we apply the division lemma to 7538 and 1704, to get
7538 = 1704 x 4 + 722
Step 2: Since the reminder 1704 ≠ 0, we apply division lemma to 722 and 1704, to get
1704 = 722 x 2 + 260
Step 3: We consider the new divisor 722 and the new remainder 260, and apply the division lemma to get
722 = 260 x 2 + 202
We consider the new divisor 260 and the new remainder 202,and apply the division lemma to get
260 = 202 x 1 + 58
We consider the new divisor 202 and the new remainder 58,and apply the division lemma to get
202 = 58 x 3 + 28
We consider the new divisor 58 and the new remainder 28,and apply the division lemma to get
58 = 28 x 2 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1704 and 7538 is 2
Notice that 2 = HCF(28,2) = HCF(58,28) = HCF(202,58) = HCF(260,202) = HCF(722,260) = HCF(1704,722) = HCF(7538,1704) .
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Frequently Asked Questions on HCF of 1704, 7538 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, 7538?
Answer: HCF of 1704, 7538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1704, 7538 using Euclid's Algorithm?
Answer: For arbitrary numbers 1704, 7538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.