Highest Common Factor of 1675, 2042 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 1675, 2042 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1675, 2042 is 1 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 1675, 2042 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 1675, 2042 is 1.
HCF(1675, 2042) = 1
HCF of 1675, 2042 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1675, 2042 is 1.
Highest Common Factor of 1675,2042 is 1
Step 1: Since 2042 > 1675, we apply the division lemma to 2042 and 1675, to get
2042 = 1675 x 1 + 367
Step 2: Since the reminder 1675 ≠ 0, we apply division lemma to 367 and 1675, to get
1675 = 367 x 4 + 207
Step 3: We consider the new divisor 367 and the new remainder 207, and apply the division lemma to get
367 = 207 x 1 + 160
We consider the new divisor 207 and the new remainder 160,and apply the division lemma to get
207 = 160 x 1 + 47
We consider the new divisor 160 and the new remainder 47,and apply the division lemma to get
160 = 47 x 3 + 19
We consider the new divisor 47 and the new remainder 19,and apply the division lemma to get
47 = 19 x 2 + 9
We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get
19 = 9 x 2 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1675 and 2042 is 1
Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(47,19) = HCF(160,47) = HCF(207,160) = HCF(367,207) = HCF(1675,367) = HCF(2042,1675) .
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Frequently Asked Questions on HCF of 1675, 2042 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 1675, 2042?
Answer: HCF of 1675, 2042 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1675, 2042 using Euclid's Algorithm?
Answer: For arbitrary numbers 1675, 2042 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.