Highest Common Factor of 1780, 2754 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 1780, 2754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1780, 2754 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 1780, 2754 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 1780, 2754 is 2.
HCF(1780, 2754) = 2
HCF of 1780, 2754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1780, 2754 is 2.
Highest Common Factor of 1780,2754 is 2
Step 1: Since 2754 > 1780, we apply the division lemma to 2754 and 1780, to get
2754 = 1780 x 1 + 974
Step 2: Since the reminder 1780 ≠ 0, we apply division lemma to 974 and 1780, to get
1780 = 974 x 1 + 806
Step 3: We consider the new divisor 974 and the new remainder 806, and apply the division lemma to get
974 = 806 x 1 + 168
We consider the new divisor 806 and the new remainder 168,and apply the division lemma to get
806 = 168 x 4 + 134
We consider the new divisor 168 and the new remainder 134,and apply the division lemma to get
168 = 134 x 1 + 34
We consider the new divisor 134 and the new remainder 34,and apply the division lemma to get
134 = 34 x 3 + 32
We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1780 and 2754 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(134,34) = HCF(168,134) = HCF(806,168) = HCF(974,806) = HCF(1780,974) = HCF(2754,1780) .
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Frequently Asked Questions on HCF of 1780, 2754 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 1780, 2754?
Answer: HCF of 1780, 2754 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1780, 2754 using Euclid's Algorithm?
Answer: For arbitrary numbers 1780, 2754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.