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 396, 699, 58 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 396, 699, 58 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 396, 699, 58 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 396, 699, 58 is 1.
HCF(396, 699, 58) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 396, 699, 58 is 1.
Step 1: Since 699 > 396, we apply the division lemma to 699 and 396, to get
699 = 396 x 1 + 303
Step 2: Since the reminder 396 ≠ 0, we apply division lemma to 303 and 396, to get
396 = 303 x 1 + 93
Step 3: We consider the new divisor 303 and the new remainder 93, and apply the division lemma to get
303 = 93 x 3 + 24
We consider the new divisor 93 and the new remainder 24,and apply the division lemma to get
93 = 24 x 3 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 396 and 699 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(93,24) = HCF(303,93) = HCF(396,303) = HCF(699,396) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 58 > 3, we apply the division lemma to 58 and 3, to get
58 = 3 x 19 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 58 is 1
Notice that 1 = HCF(3,1) = HCF(58,3) .
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 396, 699, 58?
Answer: HCF of 396, 699, 58 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 396, 699, 58 using Euclid's Algorithm?
Answer: For arbitrary numbers 396, 699, 58 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.