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, 36674 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 646, 36674 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 646, 36674 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, 36674 is 2.
HCF(646, 36674) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 646, 36674 is 2.
Step 1: Since 36674 > 646, we apply the division lemma to 36674 and 646, to get
36674 = 646 x 56 + 498
Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 498 and 646, to get
646 = 498 x 1 + 148
Step 3: We consider the new divisor 498 and the new remainder 148, and apply the division lemma to get
498 = 148 x 3 + 54
We consider the new divisor 148 and the new remainder 54,and apply the division lemma to get
148 = 54 x 2 + 40
We consider the new divisor 54 and the new remainder 40,and apply the division lemma to get
54 = 40 x 1 + 14
We consider the new divisor 40 and the new remainder 14,and apply the division lemma to get
40 = 14 x 2 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 646 and 36674 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(40,14) = HCF(54,40) = HCF(148,54) = HCF(498,148) = HCF(646,498) = HCF(36674,646) .
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, 36674?
Answer: HCF of 646, 36674 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 646, 36674 using Euclid's Algorithm?
Answer: For arbitrary numbers 646, 36674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.