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 493, 304, 698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 493, 304, 698 is 1 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 493, 304, 698 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 493, 304, 698 is 1.
HCF(493, 304, 698) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 493, 304, 698 is 1.
Step 1: Since 493 > 304, we apply the division lemma to 493 and 304, to get
493 = 304 x 1 + 189
Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 189 and 304, to get
304 = 189 x 1 + 115
Step 3: We consider the new divisor 189 and the new remainder 115, and apply the division lemma to get
189 = 115 x 1 + 74
We consider the new divisor 115 and the new remainder 74,and apply the division lemma to get
115 = 74 x 1 + 41
We consider the new divisor 74 and the new remainder 41,and apply the division lemma to get
74 = 41 x 1 + 33
We consider the new divisor 41 and the new remainder 33,and apply the division lemma to get
41 = 33 x 1 + 8
We consider the new divisor 33 and the new remainder 8,and apply the division lemma to get
33 = 8 x 4 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 493 and 304 is 1
Notice that 1 = HCF(8,1) = HCF(33,8) = HCF(41,33) = HCF(74,41) = HCF(115,74) = HCF(189,115) = HCF(304,189) = HCF(493,304) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 698 > 1, we apply the division lemma to 698 and 1, to get
698 = 1 x 698 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 698 is 1
Notice that 1 = HCF(698,1) .
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 493, 304, 698?
Answer: HCF of 493, 304, 698 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 493, 304, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 493, 304, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.