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 782, 810, 772, 994 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 782, 810, 772, 994 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 782, 810, 772, 994 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 782, 810, 772, 994 is 2.
HCF(782, 810, 772, 994) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 782, 810, 772, 994 is 2.
Step 1: Since 810 > 782, we apply the division lemma to 810 and 782, to get
810 = 782 x 1 + 28
Step 2: Since the reminder 782 ≠ 0, we apply division lemma to 28 and 782, to get
782 = 28 x 27 + 26
Step 3: We consider the new divisor 28 and the new remainder 26, and apply the division lemma to get
28 = 26 x 1 + 2
We consider the new divisor 26 and the new remainder 2, and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 782 and 810 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(782,28) = HCF(810,782) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 772 > 2, we apply the division lemma to 772 and 2, to get
772 = 2 x 386 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 772 is 2
Notice that 2 = HCF(772,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 994 > 2, we apply the division lemma to 994 and 2, to get
994 = 2 x 497 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 994 is 2
Notice that 2 = HCF(994,2) .
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 782, 810, 772, 994?
Answer: HCF of 782, 810, 772, 994 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 782, 810, 772, 994 using Euclid's Algorithm?
Answer: For arbitrary numbers 782, 810, 772, 994 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.