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 505, 831, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 831, 67 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 505, 831, 67 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 505, 831, 67 is 1.
HCF(505, 831, 67) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 831, 67 is 1.
Step 1: Since 831 > 505, we apply the division lemma to 831 and 505, to get
831 = 505 x 1 + 326
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 326 and 505, to get
505 = 326 x 1 + 179
Step 3: We consider the new divisor 326 and the new remainder 179, and apply the division lemma to get
326 = 179 x 1 + 147
We consider the new divisor 179 and the new remainder 147,and apply the division lemma to get
179 = 147 x 1 + 32
We consider the new divisor 147 and the new remainder 32,and apply the division lemma to get
147 = 32 x 4 + 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 505 and 831 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) = HCF(147,32) = HCF(179,147) = HCF(326,179) = HCF(505,326) = HCF(831,505) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 1, we apply the division lemma to 67 and 1, to get
67 = 1 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67 is 1
Notice that 1 = HCF(67,1) .
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 505, 831, 67?
Answer: HCF of 505, 831, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 831, 67 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 831, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.