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 696, 462, 978, 796 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 696, 462, 978, 796 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 696, 462, 978, 796 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 696, 462, 978, 796 is 2.
HCF(696, 462, 978, 796) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 696, 462, 978, 796 is 2.
Step 1: Since 696 > 462, we apply the division lemma to 696 and 462, to get
696 = 462 x 1 + 234
Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 234 and 462, to get
462 = 234 x 1 + 228
Step 3: We consider the new divisor 234 and the new remainder 228, and apply the division lemma to get
234 = 228 x 1 + 6
We consider the new divisor 228 and the new remainder 6, and apply the division lemma to get
228 = 6 x 38 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 696 and 462 is 6
Notice that 6 = HCF(228,6) = HCF(234,228) = HCF(462,234) = HCF(696,462) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 6, we apply the division lemma to 978 and 6, to get
978 = 6 x 163 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 978 is 6
Notice that 6 = HCF(978,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 796 > 6, we apply the division lemma to 796 and 6, to get
796 = 6 x 132 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 796 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(796,6) .
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 696, 462, 978, 796?
Answer: HCF of 696, 462, 978, 796 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 696, 462, 978, 796 using Euclid's Algorithm?
Answer: For arbitrary numbers 696, 462, 978, 796 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.