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 766, 984, 576 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 766, 984, 576 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 766, 984, 576 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 766, 984, 576 is 2.
HCF(766, 984, 576) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 766, 984, 576 is 2.
Step 1: Since 984 > 766, we apply the division lemma to 984 and 766, to get
984 = 766 x 1 + 218
Step 2: Since the reminder 766 ≠ 0, we apply division lemma to 218 and 766, to get
766 = 218 x 3 + 112
Step 3: We consider the new divisor 218 and the new remainder 112, and apply the division lemma to get
218 = 112 x 1 + 106
We consider the new divisor 112 and the new remainder 106,and apply the division lemma to get
112 = 106 x 1 + 6
We consider the new divisor 106 and the new remainder 6,and apply the division lemma to get
106 = 6 x 17 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 766 and 984 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(106,6) = HCF(112,106) = HCF(218,112) = HCF(766,218) = HCF(984,766) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 576 > 2, we apply the division lemma to 576 and 2, to get
576 = 2 x 288 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 576 is 2
Notice that 2 = HCF(576,2) .
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 766, 984, 576?
Answer: HCF of 766, 984, 576 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 766, 984, 576 using Euclid's Algorithm?
Answer: For arbitrary numbers 766, 984, 576 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.