Highest Common Factor of 1749, 1362 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 1749, 1362 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1749, 1362 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 1749, 1362 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 1749, 1362 is 3.
HCF(1749, 1362) = 3
HCF of 1749, 1362 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1749, 1362 is 3.
Highest Common Factor of 1749,1362 is 3
Step 1: Since 1749 > 1362, we apply the division lemma to 1749 and 1362, to get
1749 = 1362 x 1 + 387
Step 2: Since the reminder 1362 ≠ 0, we apply division lemma to 387 and 1362, to get
1362 = 387 x 3 + 201
Step 3: We consider the new divisor 387 and the new remainder 201, and apply the division lemma to get
387 = 201 x 1 + 186
We consider the new divisor 201 and the new remainder 186,and apply the division lemma to get
201 = 186 x 1 + 15
We consider the new divisor 186 and the new remainder 15,and apply the division lemma to get
186 = 15 x 12 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 1749 and 1362 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(186,15) = HCF(201,186) = HCF(387,201) = HCF(1362,387) = HCF(1749,1362) .
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Frequently Asked Questions on HCF of 1749, 1362 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 1749, 1362?
Answer: HCF of 1749, 1362 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1749, 1362 using Euclid's Algorithm?
Answer: For arbitrary numbers 1749, 1362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.