Highest Common Factor of 970, 7454, 2256 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 970, 7454, 2256 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 970, 7454, 2256 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 970, 7454, 2256 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 970, 7454, 2256 is 2.
HCF(970, 7454, 2256) = 2
HCF of 970, 7454, 2256 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 970, 7454, 2256 is 2.
Highest Common Factor of 970,7454,2256 is 2
Step 1: Since 7454 > 970, we apply the division lemma to 7454 and 970, to get
7454 = 970 x 7 + 664
Step 2: Since the reminder 970 ≠ 0, we apply division lemma to 664 and 970, to get
970 = 664 x 1 + 306
Step 3: We consider the new divisor 664 and the new remainder 306, and apply the division lemma to get
664 = 306 x 2 + 52
We consider the new divisor 306 and the new remainder 52,and apply the division lemma to get
306 = 52 x 5 + 46
We consider the new divisor 52 and the new remainder 46,and apply the division lemma to get
52 = 46 x 1 + 6
We consider the new divisor 46 and the new remainder 6,and apply the division lemma to get
46 = 6 x 7 + 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 970 and 7454 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(46,6) = HCF(52,46) = HCF(306,52) = HCF(664,306) = HCF(970,664) = HCF(7454,970) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2256 > 2, we apply the division lemma to 2256 and 2, to get
2256 = 2 x 1128 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 2256 is 2
Notice that 2 = HCF(2256,2) .
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Frequently Asked Questions on HCF of 970, 7454, 2256 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 970, 7454, 2256?
Answer: HCF of 970, 7454, 2256 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 970, 7454, 2256 using Euclid's Algorithm?
Answer: For arbitrary numbers 970, 7454, 2256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.