Highest Common Factor of 1767, 2160 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 1767, 2160 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1767, 2160 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 1767, 2160 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 1767, 2160 is 3.
HCF(1767, 2160) = 3
HCF of 1767, 2160 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1767, 2160 is 3.
Highest Common Factor of 1767,2160 is 3
Step 1: Since 2160 > 1767, we apply the division lemma to 2160 and 1767, to get
2160 = 1767 x 1 + 393
Step 2: Since the reminder 1767 ≠ 0, we apply division lemma to 393 and 1767, to get
1767 = 393 x 4 + 195
Step 3: We consider the new divisor 393 and the new remainder 195, and apply the division lemma to get
393 = 195 x 2 + 3
We consider the new divisor 195 and the new remainder 3, and apply the division lemma to get
195 = 3 x 65 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1767 and 2160 is 3
Notice that 3 = HCF(195,3) = HCF(393,195) = HCF(1767,393) = HCF(2160,1767) .
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Frequently Asked Questions on HCF of 1767, 2160 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 1767, 2160?
Answer: HCF of 1767, 2160 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1767, 2160 using Euclid's Algorithm?
Answer: For arbitrary numbers 1767, 2160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.