Highest Common Factor of 1764, 2075 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 1764, 2075 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1764, 2075 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 1764, 2075 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 1764, 2075 is 1.
HCF(1764, 2075) = 1
HCF of 1764, 2075 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1764, 2075 is 1.
Highest Common Factor of 1764,2075 is 1
Step 1: Since 2075 > 1764, we apply the division lemma to 2075 and 1764, to get
2075 = 1764 x 1 + 311
Step 2: Since the reminder 1764 ≠ 0, we apply division lemma to 311 and 1764, to get
1764 = 311 x 5 + 209
Step 3: We consider the new divisor 311 and the new remainder 209, and apply the division lemma to get
311 = 209 x 1 + 102
We consider the new divisor 209 and the new remainder 102,and apply the division lemma to get
209 = 102 x 2 + 5
We consider the new divisor 102 and the new remainder 5,and apply the division lemma to get
102 = 5 x 20 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1764 and 2075 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(102,5) = HCF(209,102) = HCF(311,209) = HCF(1764,311) = HCF(2075,1764) .
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Frequently Asked Questions on HCF of 1764, 2075 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 1764, 2075?
Answer: HCF of 1764, 2075 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1764, 2075 using Euclid's Algorithm?
Answer: For arbitrary numbers 1764, 2075 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.