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 842, 591, 45, 758 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 842, 591, 45, 758 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 842, 591, 45, 758 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 842, 591, 45, 758 is 1.
HCF(842, 591, 45, 758) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 842, 591, 45, 758 is 1.
Step 1: Since 842 > 591, we apply the division lemma to 842 and 591, to get
842 = 591 x 1 + 251
Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 251 and 591, to get
591 = 251 x 2 + 89
Step 3: We consider the new divisor 251 and the new remainder 89, and apply the division lemma to get
251 = 89 x 2 + 73
We consider the new divisor 89 and the new remainder 73,and apply the division lemma to get
89 = 73 x 1 + 16
We consider the new divisor 73 and the new remainder 16,and apply the division lemma to get
73 = 16 x 4 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 842 and 591 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(73,16) = HCF(89,73) = HCF(251,89) = HCF(591,251) = HCF(842,591) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 758 > 1, we apply the division lemma to 758 and 1, to get
758 = 1 x 758 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 758 is 1
Notice that 1 = HCF(758,1) .
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 842, 591, 45, 758?
Answer: HCF of 842, 591, 45, 758 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 842, 591, 45, 758 using Euclid's Algorithm?
Answer: For arbitrary numbers 842, 591, 45, 758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.