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 9712, 1256 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 9712, 1256 is 8 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 9712, 1256 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 9712, 1256 is 8.
HCF(9712, 1256) = 8
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9712, 1256 is 8.
Step 1: Since 9712 > 1256, we apply the division lemma to 9712 and 1256, to get
9712 = 1256 x 7 + 920
Step 2: Since the reminder 1256 ≠ 0, we apply division lemma to 920 and 1256, to get
1256 = 920 x 1 + 336
Step 3: We consider the new divisor 920 and the new remainder 336, and apply the division lemma to get
920 = 336 x 2 + 248
We consider the new divisor 336 and the new remainder 248,and apply the division lemma to get
336 = 248 x 1 + 88
We consider the new divisor 248 and the new remainder 88,and apply the division lemma to get
248 = 88 x 2 + 72
We consider the new divisor 88 and the new remainder 72,and apply the division lemma to get
88 = 72 x 1 + 16
We consider the new divisor 72 and the new remainder 16,and apply the division lemma to get
72 = 16 x 4 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 9712 and 1256 is 8
Notice that 8 = HCF(16,8) = HCF(72,16) = HCF(88,72) = HCF(248,88) = HCF(336,248) = HCF(920,336) = HCF(1256,920) = HCF(9712,1256) .
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 9712, 1256?
Answer: HCF of 9712, 1256 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9712, 1256 using Euclid's Algorithm?
Answer: For arbitrary numbers 9712, 1256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.