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 310, 760, 766 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 760, 766 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 310, 760, 766 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 310, 760, 766 is 2.
HCF(310, 760, 766) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 760, 766 is 2.
Step 1: Since 760 > 310, we apply the division lemma to 760 and 310, to get
760 = 310 x 2 + 140
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 140 and 310, to get
310 = 140 x 2 + 30
Step 3: We consider the new divisor 140 and the new remainder 30, and apply the division lemma to get
140 = 30 x 4 + 20
We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 310 and 760 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(140,30) = HCF(310,140) = HCF(760,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 766 > 10, we apply the division lemma to 766 and 10, to get
766 = 10 x 76 + 6
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 6 and 10, to get
10 = 6 x 1 + 4
Step 3: 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 10 and 766 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(766,10) .
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 310, 760, 766?
Answer: HCF of 310, 760, 766 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 760, 766 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 760, 766 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.