Highest Common Factor of 506, 194, 744 using Euclid's algorithm
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 506, 194, 744 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 194, 744 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 506, 194, 744 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 506, 194, 744 is 2.
HCF(506, 194, 744) = 2
HCF of 506, 194, 744 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 194, 744 is 2.
Highest Common Factor of 506,194,744 is 2
Step 1: Since 506 > 194, we apply the division lemma to 506 and 194, to get
506 = 194 x 2 + 118
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 118 and 194, to get
194 = 118 x 1 + 76
Step 3: We consider the new divisor 118 and the new remainder 76, and apply the division lemma to get
118 = 76 x 1 + 42
We consider the new divisor 76 and the new remainder 42,and apply the division lemma to get
76 = 42 x 1 + 34
We consider the new divisor 42 and the new remainder 34,and apply the division lemma to get
42 = 34 x 1 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 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 506 and 194 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(42,34) = HCF(76,42) = HCF(118,76) = HCF(194,118) = HCF(506,194) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 744 > 2, we apply the division lemma to 744 and 2, to get
744 = 2 x 372 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 744 is 2
Notice that 2 = HCF(744,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 506, 194, 744 using Euclid's Algorithm
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 506, 194, 744?
Answer: HCF of 506, 194, 744 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 194, 744 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 194, 744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.