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 772, 606, 418 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 772, 606, 418 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 772, 606, 418 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 772, 606, 418 is 2.
HCF(772, 606, 418) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 772, 606, 418 is 2.
Step 1: Since 772 > 606, we apply the division lemma to 772 and 606, to get
772 = 606 x 1 + 166
Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 166 and 606, to get
606 = 166 x 3 + 108
Step 3: We consider the new divisor 166 and the new remainder 108, and apply the division lemma to get
166 = 108 x 1 + 58
We consider the new divisor 108 and the new remainder 58,and apply the division lemma to get
108 = 58 x 1 + 50
We consider the new divisor 58 and the new remainder 50,and apply the division lemma to get
58 = 50 x 1 + 8
We consider the new divisor 50 and the new remainder 8,and apply the division lemma to get
50 = 8 x 6 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 772 and 606 is 2
Notice that 2 = HCF(8,2) = HCF(50,8) = HCF(58,50) = HCF(108,58) = HCF(166,108) = HCF(606,166) = HCF(772,606) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 418 > 2, we apply the division lemma to 418 and 2, to get
418 = 2 x 209 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 418 is 2
Notice that 2 = HCF(418,2) .
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 772, 606, 418?
Answer: HCF of 772, 606, 418 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 772, 606, 418 using Euclid's Algorithm?
Answer: For arbitrary numbers 772, 606, 418 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.