Highest Common Factor of 7274, 7100 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 7274, 7100 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7274, 7100 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 7274, 7100 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 7274, 7100 is 2.
HCF(7274, 7100) = 2
HCF of 7274, 7100 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7274, 7100 is 2.
Highest Common Factor of 7274,7100 is 2
Step 1: Since 7274 > 7100, we apply the division lemma to 7274 and 7100, to get
7274 = 7100 x 1 + 174
Step 2: Since the reminder 7100 ≠ 0, we apply division lemma to 174 and 7100, to get
7100 = 174 x 40 + 140
Step 3: We consider the new divisor 174 and the new remainder 140, and apply the division lemma to get
174 = 140 x 1 + 34
We consider the new divisor 140 and the new remainder 34,and apply the division lemma to get
140 = 34 x 4 + 4
We consider the new divisor 34 and the new remainder 4,and apply the division lemma to get
34 = 4 x 8 + 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 7274 and 7100 is 2
Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(140,34) = HCF(174,140) = HCF(7100,174) = HCF(7274,7100) .
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Frequently Asked Questions on HCF of 7274, 7100 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 7274, 7100?
Answer: HCF of 7274, 7100 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7274, 7100 using Euclid's Algorithm?
Answer: For arbitrary numbers 7274, 7100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.