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 834, 598, 993 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 834, 598, 993 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 834, 598, 993 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 834, 598, 993 is 1.
HCF(834, 598, 993) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 834, 598, 993 is 1.
Step 1: Since 834 > 598, we apply the division lemma to 834 and 598, to get
834 = 598 x 1 + 236
Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 236 and 598, to get
598 = 236 x 2 + 126
Step 3: We consider the new divisor 236 and the new remainder 126, and apply the division lemma to get
236 = 126 x 1 + 110
We consider the new divisor 126 and the new remainder 110,and apply the division lemma to get
126 = 110 x 1 + 16
We consider the new divisor 110 and the new remainder 16,and apply the division lemma to get
110 = 16 x 6 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 834 and 598 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(110,16) = HCF(126,110) = HCF(236,126) = HCF(598,236) = HCF(834,598) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 993 > 2, we apply the division lemma to 993 and 2, to get
993 = 2 x 496 + 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 993 is 1
Notice that 1 = HCF(2,1) = HCF(993,2) .
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 834, 598, 993?
Answer: HCF of 834, 598, 993 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 834, 598, 993 using Euclid's Algorithm?
Answer: For arbitrary numbers 834, 598, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.