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 491, 676, 543, 742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 491, 676, 543, 742 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 491, 676, 543, 742 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 491, 676, 543, 742 is 1.
HCF(491, 676, 543, 742) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 491, 676, 543, 742 is 1.
Step 1: Since 676 > 491, we apply the division lemma to 676 and 491, to get
676 = 491 x 1 + 185
Step 2: Since the reminder 491 ≠ 0, we apply division lemma to 185 and 491, to get
491 = 185 x 2 + 121
Step 3: We consider the new divisor 185 and the new remainder 121, and apply the division lemma to get
185 = 121 x 1 + 64
We consider the new divisor 121 and the new remainder 64,and apply the division lemma to get
121 = 64 x 1 + 57
We consider the new divisor 64 and the new remainder 57,and apply the division lemma to get
64 = 57 x 1 + 7
We consider the new divisor 57 and the new remainder 7,and apply the division lemma to get
57 = 7 x 8 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 491 and 676 is 1
Notice that 1 = HCF(7,1) = HCF(57,7) = HCF(64,57) = HCF(121,64) = HCF(185,121) = HCF(491,185) = HCF(676,491) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 543 > 1, we apply the division lemma to 543 and 1, to get
543 = 1 x 543 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 543 is 1
Notice that 1 = HCF(543,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 742 > 1, we apply the division lemma to 742 and 1, to get
742 = 1 x 742 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 742 is 1
Notice that 1 = HCF(742,1) .
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 491, 676, 543, 742?
Answer: HCF of 491, 676, 543, 742 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 491, 676, 543, 742 using Euclid's Algorithm?
Answer: For arbitrary numbers 491, 676, 543, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.