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 782, 570, 163, 193 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 782, 570, 163, 193 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 782, 570, 163, 193 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 782, 570, 163, 193 is 1.
HCF(782, 570, 163, 193) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 782, 570, 163, 193 is 1.
Step 1: Since 782 > 570, we apply the division lemma to 782 and 570, to get
782 = 570 x 1 + 212
Step 2: Since the reminder 570 ≠ 0, we apply division lemma to 212 and 570, to get
570 = 212 x 2 + 146
Step 3: We consider the new divisor 212 and the new remainder 146, and apply the division lemma to get
212 = 146 x 1 + 66
We consider the new divisor 146 and the new remainder 66,and apply the division lemma to get
146 = 66 x 2 + 14
We consider the new divisor 66 and the new remainder 14,and apply the division lemma to get
66 = 14 x 4 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 782 and 570 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) = HCF(146,66) = HCF(212,146) = HCF(570,212) = HCF(782,570) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 163 > 2, we apply the division lemma to 163 and 2, to get
163 = 2 x 81 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 163 is 1
Notice that 1 = HCF(2,1) = HCF(163,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 193 > 1, we apply the division lemma to 193 and 1, to get
193 = 1 x 193 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 193 is 1
Notice that 1 = HCF(193,1) .
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 782, 570, 163, 193?
Answer: HCF of 782, 570, 163, 193 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 782, 570, 163, 193 using Euclid's Algorithm?
Answer: For arbitrary numbers 782, 570, 163, 193 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.