Highest Common Factor of 738, 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 738, 7100 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 738, 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 738, 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 738, 7100 is 2.
HCF(738, 7100) = 2
HCF of 738, 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 738, 7100 is 2.
Highest Common Factor of 738,7100 is 2
Step 1: Since 7100 > 738, we apply the division lemma to 7100 and 738, to get
7100 = 738 x 9 + 458
Step 2: Since the reminder 738 ≠ 0, we apply division lemma to 458 and 738, to get
738 = 458 x 1 + 280
Step 3: We consider the new divisor 458 and the new remainder 280, and apply the division lemma to get
458 = 280 x 1 + 178
We consider the new divisor 280 and the new remainder 178,and apply the division lemma to get
280 = 178 x 1 + 102
We consider the new divisor 178 and the new remainder 102,and apply the division lemma to get
178 = 102 x 1 + 76
We consider the new divisor 102 and the new remainder 76,and apply the division lemma to get
102 = 76 x 1 + 26
We consider the new divisor 76 and the new remainder 26,and apply the division lemma to get
76 = 26 x 2 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 738 and 7100 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(76,26) = HCF(102,76) = HCF(178,102) = HCF(280,178) = HCF(458,280) = HCF(738,458) = HCF(7100,738) .
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Frequently Asked Questions on HCF of 738, 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 738, 7100?
Answer: HCF of 738, 7100 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 738, 7100 using Euclid's Algorithm?
Answer: For arbitrary numbers 738, 7100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.