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 319, 823, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 319, 823, 649 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 319, 823, 649 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 319, 823, 649 is 1.
HCF(319, 823, 649) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 319, 823, 649 is 1.
Step 1: Since 823 > 319, we apply the division lemma to 823 and 319, to get
823 = 319 x 2 + 185
Step 2: Since the reminder 319 ≠ 0, we apply division lemma to 185 and 319, to get
319 = 185 x 1 + 134
Step 3: We consider the new divisor 185 and the new remainder 134, and apply the division lemma to get
185 = 134 x 1 + 51
We consider the new divisor 134 and the new remainder 51,and apply the division lemma to get
134 = 51 x 2 + 32
We consider the new divisor 51 and the new remainder 32,and apply the division lemma to get
51 = 32 x 1 + 19
We consider the new divisor 32 and the new remainder 19,and apply the division lemma to get
32 = 19 x 1 + 13
We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 319 and 823 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) = HCF(51,32) = HCF(134,51) = HCF(185,134) = HCF(319,185) = HCF(823,319) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 649 > 1, we apply the division lemma to 649 and 1, to get
649 = 1 x 649 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 649 is 1
Notice that 1 = HCF(649,1) .
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 319, 823, 649?
Answer: HCF of 319, 823, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 319, 823, 649 using Euclid's Algorithm?
Answer: For arbitrary numbers 319, 823, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.