Highest Common Factor of 2974, 1864 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 2974, 1864 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2974, 1864 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 2974, 1864 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 2974, 1864 is 2.
HCF(2974, 1864) = 2
HCF of 2974, 1864 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2974, 1864 is 2.
Highest Common Factor of 2974,1864 is 2
Step 1: Since 2974 > 1864, we apply the division lemma to 2974 and 1864, to get
2974 = 1864 x 1 + 1110
Step 2: Since the reminder 1864 ≠ 0, we apply division lemma to 1110 and 1864, to get
1864 = 1110 x 1 + 754
Step 3: We consider the new divisor 1110 and the new remainder 754, and apply the division lemma to get
1110 = 754 x 1 + 356
We consider the new divisor 754 and the new remainder 356,and apply the division lemma to get
754 = 356 x 2 + 42
We consider the new divisor 356 and the new remainder 42,and apply the division lemma to get
356 = 42 x 8 + 20
We consider the new divisor 42 and the new remainder 20,and apply the division lemma to get
42 = 20 x 2 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2974 and 1864 is 2
Notice that 2 = HCF(20,2) = HCF(42,20) = HCF(356,42) = HCF(754,356) = HCF(1110,754) = HCF(1864,1110) = HCF(2974,1864) .
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Frequently Asked Questions on HCF of 2974, 1864 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 2974, 1864?
Answer: HCF of 2974, 1864 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2974, 1864 using Euclid's Algorithm?
Answer: For arbitrary numbers 2974, 1864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.