Highest Common Factor of 744, 440, 407 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 744, 440, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 744, 440, 407 is 1 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 744, 440, 407 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 744, 440, 407 is 1.
HCF(744, 440, 407) = 1
HCF of 744, 440, 407 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 744, 440, 407 is 1.
Highest Common Factor of 744,440,407 is 1
Step 1: Since 744 > 440, we apply the division lemma to 744 and 440, to get
744 = 440 x 1 + 304
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 304 and 440, to get
440 = 304 x 1 + 136
Step 3: We consider the new divisor 304 and the new remainder 136, and apply the division lemma to get
304 = 136 x 2 + 32
We consider the new divisor 136 and the new remainder 32,and apply the division lemma to get
136 = 32 x 4 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 744 and 440 is 8
Notice that 8 = HCF(32,8) = HCF(136,32) = HCF(304,136) = HCF(440,304) = HCF(744,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 8, we apply the division lemma to 407 and 8, to get
407 = 8 x 50 + 7
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 7 and 8, to get
8 = 7 x 1 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 407 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(407,8) .
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Frequently Asked Questions on HCF of 744, 440, 407 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 744, 440, 407?
Answer: HCF of 744, 440, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 744, 440, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 744, 440, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.