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 159, 774, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 159, 774, 218 is 1 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 159, 774, 218 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 159, 774, 218 is 1.
HCF(159, 774, 218) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 159, 774, 218 is 1.
Step 1: Since 774 > 159, we apply the division lemma to 774 and 159, to get
774 = 159 x 4 + 138
Step 2: Since the reminder 159 ≠ 0, we apply division lemma to 138 and 159, to get
159 = 138 x 1 + 21
Step 3: We consider the new divisor 138 and the new remainder 21, and apply the division lemma to get
138 = 21 x 6 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 159 and 774 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(138,21) = HCF(159,138) = HCF(774,159) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 218 > 3, we apply the division lemma to 218 and 3, to get
218 = 3 x 72 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 218 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(218,3) .
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 159, 774, 218?
Answer: HCF of 159, 774, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 159, 774, 218 using Euclid's Algorithm?
Answer: For arbitrary numbers 159, 774, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.