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 9762, 2954 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9762, 2954 is 2 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 9762, 2954 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 9762, 2954 is 2.
HCF(9762, 2954) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9762, 2954 is 2.
Step 1: Since 9762 > 2954, we apply the division lemma to 9762 and 2954, to get
9762 = 2954 x 3 + 900
Step 2: Since the reminder 2954 ≠ 0, we apply division lemma to 900 and 2954, to get
2954 = 900 x 3 + 254
Step 3: We consider the new divisor 900 and the new remainder 254, and apply the division lemma to get
900 = 254 x 3 + 138
We consider the new divisor 254 and the new remainder 138,and apply the division lemma to get
254 = 138 x 1 + 116
We consider the new divisor 138 and the new remainder 116,and apply the division lemma to get
138 = 116 x 1 + 22
We consider the new divisor 116 and the new remainder 22,and apply the division lemma to get
116 = 22 x 5 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9762 and 2954 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(116,22) = HCF(138,116) = HCF(254,138) = HCF(900,254) = HCF(2954,900) = HCF(9762,2954) .
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 9762, 2954?
Answer: HCF of 9762, 2954 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9762, 2954 using Euclid's Algorithm?
Answer: For arbitrary numbers 9762, 2954 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.