Highest Common Factor of 1987, 2457 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 1987, 2457 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1987, 2457 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 1987, 2457 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 1987, 2457 is 1.
HCF(1987, 2457) = 1
HCF of 1987, 2457 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1987, 2457 is 1.
Highest Common Factor of 1987,2457 is 1
Step 1: Since 2457 > 1987, we apply the division lemma to 2457 and 1987, to get
2457 = 1987 x 1 + 470
Step 2: Since the reminder 1987 ≠ 0, we apply division lemma to 470 and 1987, to get
1987 = 470 x 4 + 107
Step 3: We consider the new divisor 470 and the new remainder 107, and apply the division lemma to get
470 = 107 x 4 + 42
We consider the new divisor 107 and the new remainder 42,and apply the division lemma to get
107 = 42 x 2 + 23
We consider the new divisor 42 and the new remainder 23,and apply the division lemma to get
42 = 23 x 1 + 19
We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get
23 = 19 x 1 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1987 and 2457 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(42,23) = HCF(107,42) = HCF(470,107) = HCF(1987,470) = HCF(2457,1987) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1987, 2457 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 1987, 2457?
Answer: HCF of 1987, 2457 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1987, 2457 using Euclid's Algorithm?
Answer: For arbitrary numbers 1987, 2457 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.