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 774, 425, 491 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 425, 491 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 774, 425, 491 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 774, 425, 491 is 1.
HCF(774, 425, 491) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 425, 491 is 1.
Step 1: Since 774 > 425, we apply the division lemma to 774 and 425, to get
774 = 425 x 1 + 349
Step 2: Since the reminder 425 ≠ 0, we apply division lemma to 349 and 425, to get
425 = 349 x 1 + 76
Step 3: We consider the new divisor 349 and the new remainder 76, and apply the division lemma to get
349 = 76 x 4 + 45
We consider the new divisor 76 and the new remainder 45,and apply the division lemma to get
76 = 45 x 1 + 31
We consider the new divisor 45 and the new remainder 31,and apply the division lemma to get
45 = 31 x 1 + 14
We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get
31 = 14 x 2 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 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 774 and 425 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(45,31) = HCF(76,45) = HCF(349,76) = HCF(425,349) = HCF(774,425) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 491 > 1, we apply the division lemma to 491 and 1, to get
491 = 1 x 491 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 491 is 1
Notice that 1 = HCF(491,1) .
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 774, 425, 491?
Answer: HCF of 774, 425, 491 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 425, 491 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 425, 491 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.