Highest Common Factor of 742, 1744, 2440 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 742, 1744, 2440 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 1744, 2440 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 742, 1744, 2440 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 742, 1744, 2440 is 2.
HCF(742, 1744, 2440) = 2
HCF of 742, 1744, 2440 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 1744, 2440 is 2.
Highest Common Factor of 742,1744,2440 is 2
Step 1: Since 1744 > 742, we apply the division lemma to 1744 and 742, to get
1744 = 742 x 2 + 260
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 260 and 742, to get
742 = 260 x 2 + 222
Step 3: We consider the new divisor 260 and the new remainder 222, and apply the division lemma to get
260 = 222 x 1 + 38
We consider the new divisor 222 and the new remainder 38,and apply the division lemma to get
222 = 38 x 5 + 32
We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get
38 = 32 x 1 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 2
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 742 and 1744 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(222,38) = HCF(260,222) = HCF(742,260) = HCF(1744,742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2440 > 2, we apply the division lemma to 2440 and 2, to get
2440 = 2 x 1220 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 2440 is 2
Notice that 2 = HCF(2440,2) .
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Frequently Asked Questions on HCF of 742, 1744, 2440 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 742, 1744, 2440?
Answer: HCF of 742, 1744, 2440 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 1744, 2440 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 1744, 2440 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
