Highest Common Factor of 196, 744, 454 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 196, 744, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 196, 744, 454 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 196, 744, 454 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 196, 744, 454 is 2.
HCF(196, 744, 454) = 2
HCF of 196, 744, 454 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 196, 744, 454 is 2.
Highest Common Factor of 196,744,454 is 2
Step 1: Since 744 > 196, we apply the division lemma to 744 and 196, to get
744 = 196 x 3 + 156
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 156 and 196, to get
196 = 156 x 1 + 40
Step 3: We consider the new divisor 156 and the new remainder 40, and apply the division lemma to get
156 = 40 x 3 + 36
We consider the new divisor 40 and the new remainder 36,and apply the division lemma to get
40 = 36 x 1 + 4
We consider the new divisor 36 and the new remainder 4,and apply the division lemma to get
36 = 4 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 196 and 744 is 4
Notice that 4 = HCF(36,4) = HCF(40,36) = HCF(156,40) = HCF(196,156) = HCF(744,196) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 454 > 4, we apply the division lemma to 454 and 4, to get
454 = 4 x 113 + 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 454 is 2
Notice that 2 = HCF(4,2) = HCF(454,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 196, 744, 454 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 196, 744, 454?
Answer: HCF of 196, 744, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 196, 744, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 196, 744, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.