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 812, 502, 774, 216 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 502, 774, 216 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 812, 502, 774, 216 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 812, 502, 774, 216 is 2.
HCF(812, 502, 774, 216) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 502, 774, 216 is 2.
Step 1: Since 812 > 502, we apply the division lemma to 812 and 502, to get
812 = 502 x 1 + 310
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 310 and 502, to get
502 = 310 x 1 + 192
Step 3: We consider the new divisor 310 and the new remainder 192, and apply the division lemma to get
310 = 192 x 1 + 118
We consider the new divisor 192 and the new remainder 118,and apply the division lemma to get
192 = 118 x 1 + 74
We consider the new divisor 118 and the new remainder 74,and apply the division lemma to get
118 = 74 x 1 + 44
We consider the new divisor 74 and the new remainder 44,and apply the division lemma to get
74 = 44 x 1 + 30
We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get
44 = 30 x 1 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 812 and 502 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(74,44) = HCF(118,74) = HCF(192,118) = HCF(310,192) = HCF(502,310) = HCF(812,502) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 774 > 2, we apply the division lemma to 774 and 2, to get
774 = 2 x 387 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 774 is 2
Notice that 2 = HCF(774,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 216 > 2, we apply the division lemma to 216 and 2, to get
216 = 2 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 216 is 2
Notice that 2 = HCF(216,2) .
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 812, 502, 774, 216?
Answer: HCF of 812, 502, 774, 216 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 502, 774, 216 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 502, 774, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.