Highest Common Factor of 694, 490, 54 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 694, 490, 54 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 694, 490, 54 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 694, 490, 54 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 694, 490, 54 is 2.
HCF(694, 490, 54) = 2
HCF of 694, 490, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 694, 490, 54 is 2.
Highest Common Factor of 694,490,54 is 2
Step 1: Since 694 > 490, we apply the division lemma to 694 and 490, to get
694 = 490 x 1 + 204
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 204 and 490, to get
490 = 204 x 2 + 82
Step 3: We consider the new divisor 204 and the new remainder 82, and apply the division lemma to get
204 = 82 x 2 + 40
We consider the new divisor 82 and the new remainder 40,and apply the division lemma to get
82 = 40 x 2 + 2
We consider the new divisor 40 and the new remainder 2,and apply the division lemma to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 694 and 490 is 2
Notice that 2 = HCF(40,2) = HCF(82,40) = HCF(204,82) = HCF(490,204) = HCF(694,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 2, we apply the division lemma to 54 and 2, to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 54 is 2
Notice that 2 = HCF(54,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 694, 490, 54 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 694, 490, 54?
Answer: HCF of 694, 490, 54 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 694, 490, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 694, 490, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.