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 646, 998, 231 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 646, 998, 231 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 646, 998, 231 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 646, 998, 231 is 1.
HCF(646, 998, 231) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 646, 998, 231 is 1.
Step 1: Since 998 > 646, we apply the division lemma to 998 and 646, to get
998 = 646 x 1 + 352
Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 352 and 646, to get
646 = 352 x 1 + 294
Step 3: We consider the new divisor 352 and the new remainder 294, and apply the division lemma to get
352 = 294 x 1 + 58
We consider the new divisor 294 and the new remainder 58,and apply the division lemma to get
294 = 58 x 5 + 4
We consider the new divisor 58 and the new remainder 4,and apply the division lemma to get
58 = 4 x 14 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 646 and 998 is 2
Notice that 2 = HCF(4,2) = HCF(58,4) = HCF(294,58) = HCF(352,294) = HCF(646,352) = HCF(998,646) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 231 > 2, we apply the division lemma to 231 and 2, to get
231 = 2 x 115 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 231 is 1
Notice that 1 = HCF(2,1) = HCF(231,2) .
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 646, 998, 231?
Answer: HCF of 646, 998, 231 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 646, 998, 231 using Euclid's Algorithm?
Answer: For arbitrary numbers 646, 998, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.