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, 945, 258 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 834, 945, 258 is 3 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, 945, 258 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, 945, 258 is 3.
HCF(834, 945, 258) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 834, 945, 258 is 3.
Step 1: Since 945 > 834, we apply the division lemma to 945 and 834, to get
945 = 834 x 1 + 111
Step 2: Since the reminder 834 ≠ 0, we apply division lemma to 111 and 834, to get
834 = 111 x 7 + 57
Step 3: We consider the new divisor 111 and the new remainder 57, and apply the division lemma to get
111 = 57 x 1 + 54
We consider the new divisor 57 and the new remainder 54,and apply the division lemma to get
57 = 54 x 1 + 3
We consider the new divisor 54 and the new remainder 3,and apply the division lemma to get
54 = 3 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 834 and 945 is 3
Notice that 3 = HCF(54,3) = HCF(57,54) = HCF(111,57) = HCF(834,111) = HCF(945,834) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 258 > 3, we apply the division lemma to 258 and 3, to get
258 = 3 x 86 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 258 is 3
Notice that 3 = HCF(258,3) .
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, 945, 258?
Answer: HCF of 834, 945, 258 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 834, 945, 258 using Euclid's Algorithm?
Answer: For arbitrary numbers 834, 945, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.