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 612, 448, 502 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 448, 502 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 612, 448, 502 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 612, 448, 502 is 2.
HCF(612, 448, 502) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 448, 502 is 2.
Step 1: Since 612 > 448, we apply the division lemma to 612 and 448, to get
612 = 448 x 1 + 164
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 164 and 448, to get
448 = 164 x 2 + 120
Step 3: We consider the new divisor 164 and the new remainder 120, and apply the division lemma to get
164 = 120 x 1 + 44
We consider the new divisor 120 and the new remainder 44,and apply the division lemma to get
120 = 44 x 2 + 32
We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get
44 = 32 x 1 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 612 and 448 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(120,44) = HCF(164,120) = HCF(448,164) = HCF(612,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 502 > 4, we apply the division lemma to 502 and 4, to get
502 = 4 x 125 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 502 is 2
Notice that 2 = HCF(4,2) = HCF(502,4) .
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 612, 448, 502?
Answer: HCF of 612, 448, 502 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 448, 502 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 448, 502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.