Highest Common Factor of 256, 7240, 9934 using Euclid's algorithm
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 256, 7240, 9934 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 256, 7240, 9934 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 256, 7240, 9934 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 256, 7240, 9934 is 2.
HCF(256, 7240, 9934) = 2
HCF of 256, 7240, 9934 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 256, 7240, 9934 is 2.
Highest Common Factor of 256,7240,9934 is 2
Step 1: Since 7240 > 256, we apply the division lemma to 7240 and 256, to get
7240 = 256 x 28 + 72
Step 2: Since the reminder 256 ≠ 0, we apply division lemma to 72 and 256, to get
256 = 72 x 3 + 40
Step 3: We consider the new divisor 72 and the new remainder 40, and apply the division lemma to get
72 = 40 x 1 + 32
We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get
40 = 32 x 1 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 256 and 7240 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(72,40) = HCF(256,72) = HCF(7240,256) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9934 > 8, we apply the division lemma to 9934 and 8, to get
9934 = 8 x 1241 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 9934 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(9934,8) .
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Frequently Asked Questions on HCF of 256, 7240, 9934 using Euclid's Algorithm
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 256, 7240, 9934?
Answer: HCF of 256, 7240, 9934 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 256, 7240, 9934 using Euclid's Algorithm?
Answer: For arbitrary numbers 256, 7240, 9934 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.