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 1204, 2974 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1204, 2974 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 1204, 2974 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 1204, 2974 is 2.
HCF(1204, 2974) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1204, 2974 is 2.
Step 1: Since 2974 > 1204, we apply the division lemma to 2974 and 1204, to get
2974 = 1204 x 2 + 566
Step 2: Since the reminder 1204 ≠ 0, we apply division lemma to 566 and 1204, to get
1204 = 566 x 2 + 72
Step 3: We consider the new divisor 566 and the new remainder 72, and apply the division lemma to get
566 = 72 x 7 + 62
We consider the new divisor 72 and the new remainder 62,and apply the division lemma to get
72 = 62 x 1 + 10
We consider the new divisor 62 and the new remainder 10,and apply the division lemma to get
62 = 10 x 6 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1204 and 2974 is 2
Notice that 2 = HCF(10,2) = HCF(62,10) = HCF(72,62) = HCF(566,72) = HCF(1204,566) = HCF(2974,1204) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 1204, 2974?
Answer: HCF of 1204, 2974 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1204, 2974 using Euclid's Algorithm?
Answer: For arbitrary numbers 1204, 2974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.