Highest Common Factor of 747, 450, 414 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 747, 450, 414 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 747, 450, 414 is 9 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 747, 450, 414 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 747, 450, 414 is 9.
HCF(747, 450, 414) = 9
HCF of 747, 450, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 747, 450, 414 is 9.
Highest Common Factor of 747,450,414 is 9
Step 1: Since 747 > 450, we apply the division lemma to 747 and 450, to get
747 = 450 x 1 + 297
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 297 and 450, to get
450 = 297 x 1 + 153
Step 3: We consider the new divisor 297 and the new remainder 153, and apply the division lemma to get
297 = 153 x 1 + 144
We consider the new divisor 153 and the new remainder 144,and apply the division lemma to get
153 = 144 x 1 + 9
We consider the new divisor 144 and the new remainder 9,and apply the division lemma to get
144 = 9 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 747 and 450 is 9
Notice that 9 = HCF(144,9) = HCF(153,144) = HCF(297,153) = HCF(450,297) = HCF(747,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 9, we apply the division lemma to 414 and 9, to get
414 = 9 x 46 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 414 is 9
Notice that 9 = HCF(414,9) .
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Frequently Asked Questions on HCF of 747, 450, 414 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 747, 450, 414?
Answer: HCF of 747, 450, 414 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 747, 450, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 747, 450, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.