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 3185, 8363, 51109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3185, 8363, 51109 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 3185, 8363, 51109 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 3185, 8363, 51109 is 1.
HCF(3185, 8363, 51109) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3185, 8363, 51109 is 1.
Step 1: Since 8363 > 3185, we apply the division lemma to 8363 and 3185, to get
8363 = 3185 x 2 + 1993
Step 2: Since the reminder 3185 ≠ 0, we apply division lemma to 1993 and 3185, to get
3185 = 1993 x 1 + 1192
Step 3: We consider the new divisor 1993 and the new remainder 1192, and apply the division lemma to get
1993 = 1192 x 1 + 801
We consider the new divisor 1192 and the new remainder 801,and apply the division lemma to get
1192 = 801 x 1 + 391
We consider the new divisor 801 and the new remainder 391,and apply the division lemma to get
801 = 391 x 2 + 19
We consider the new divisor 391 and the new remainder 19,and apply the division lemma to get
391 = 19 x 20 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 3185 and 8363 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(391,19) = HCF(801,391) = HCF(1192,801) = HCF(1993,1192) = HCF(3185,1993) = HCF(8363,3185) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51109 > 1, we apply the division lemma to 51109 and 1, to get
51109 = 1 x 51109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 51109 is 1
Notice that 1 = HCF(51109,1) .
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 3185, 8363, 51109?
Answer: HCF of 3185, 8363, 51109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3185, 8363, 51109 using Euclid's Algorithm?
Answer: For arbitrary numbers 3185, 8363, 51109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.