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 778, 474, 831 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 778, 474, 831 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 778, 474, 831 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 778, 474, 831 is 1.
HCF(778, 474, 831) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 778, 474, 831 is 1.
Step 1: Since 778 > 474, we apply the division lemma to 778 and 474, to get
778 = 474 x 1 + 304
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 304 and 474, to get
474 = 304 x 1 + 170
Step 3: We consider the new divisor 304 and the new remainder 170, and apply the division lemma to get
304 = 170 x 1 + 134
We consider the new divisor 170 and the new remainder 134,and apply the division lemma to get
170 = 134 x 1 + 36
We consider the new divisor 134 and the new remainder 36,and apply the division lemma to get
134 = 36 x 3 + 26
We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get
36 = 26 x 1 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 778 and 474 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(134,36) = HCF(170,134) = HCF(304,170) = HCF(474,304) = HCF(778,474) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 831 > 2, we apply the division lemma to 831 and 2, to get
831 = 2 x 415 + 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 831 is 1
Notice that 1 = HCF(2,1) = HCF(831,2) .
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 778, 474, 831?
Answer: HCF of 778, 474, 831 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 778, 474, 831 using Euclid's Algorithm?
Answer: For arbitrary numbers 778, 474, 831 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.