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, 237 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 646, 237 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, 237 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, 237 is 1.
HCF(646, 237) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 646, 237 is 1.
Step 1: Since 646 > 237, we apply the division lemma to 646 and 237, to get
646 = 237 x 2 + 172
Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 172 and 237, to get
237 = 172 x 1 + 65
Step 3: We consider the new divisor 172 and the new remainder 65, and apply the division lemma to get
172 = 65 x 2 + 42
We consider the new divisor 65 and the new remainder 42,and apply the division lemma to get
65 = 42 x 1 + 23
We consider the new divisor 42 and the new remainder 23,and apply the division lemma to get
42 = 23 x 1 + 19
We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get
23 = 19 x 1 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 646 and 237 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(42,23) = HCF(65,42) = HCF(172,65) = HCF(237,172) = HCF(646,237) .
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, 237?
Answer: HCF of 646, 237 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 646, 237 using Euclid's Algorithm?
Answer: For arbitrary numbers 646, 237 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.