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 978, 2814, 4773 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 2814, 4773 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 978, 2814, 4773 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 978, 2814, 4773 is 3.
HCF(978, 2814, 4773) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 2814, 4773 is 3.
Step 1: Since 2814 > 978, we apply the division lemma to 2814 and 978, to get
2814 = 978 x 2 + 858
Step 2: Since the reminder 978 ≠ 0, we apply division lemma to 858 and 978, to get
978 = 858 x 1 + 120
Step 3: We consider the new divisor 858 and the new remainder 120, and apply the division lemma to get
858 = 120 x 7 + 18
We consider the new divisor 120 and the new remainder 18,and apply the division lemma to get
120 = 18 x 6 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 2814 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(120,18) = HCF(858,120) = HCF(978,858) = HCF(2814,978) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4773 > 6, we apply the division lemma to 4773 and 6, to get
4773 = 6 x 795 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 4773 is 3
Notice that 3 = HCF(6,3) = HCF(4773,6) .
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 978, 2814, 4773?
Answer: HCF of 978, 2814, 4773 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 2814, 4773 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 2814, 4773 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.