Highest Common Factor of 740, 2700 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 740, 2700 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 740, 2700 is 20 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 740, 2700 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 740, 2700 is 20.
HCF(740, 2700) = 20
HCF of 740, 2700 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 740, 2700 is 20.
Highest Common Factor of 740,2700 is 20
Step 1: Since 2700 > 740, we apply the division lemma to 2700 and 740, to get
2700 = 740 x 3 + 480
Step 2: Since the reminder 740 ≠ 0, we apply division lemma to 480 and 740, to get
740 = 480 x 1 + 260
Step 3: We consider the new divisor 480 and the new remainder 260, and apply the division lemma to get
480 = 260 x 1 + 220
We consider the new divisor 260 and the new remainder 220,and apply the division lemma to get
260 = 220 x 1 + 40
We consider the new divisor 220 and the new remainder 40,and apply the division lemma to get
220 = 40 x 5 + 20
We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 740 and 2700 is 20
Notice that 20 = HCF(40,20) = HCF(220,40) = HCF(260,220) = HCF(480,260) = HCF(740,480) = HCF(2700,740) .
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Frequently Asked Questions on HCF of 740, 2700 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 740, 2700?
Answer: HCF of 740, 2700 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 740, 2700 using Euclid's Algorithm?
Answer: For arbitrary numbers 740, 2700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.