Highest Common Factor of 754, 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 754, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 414 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 754, 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 754, 414 is 2.
HCF(754, 414) = 2
HCF of 754, 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 754, 414 is 2.
Highest Common Factor of 754,414 is 2
Step 1: Since 754 > 414, we apply the division lemma to 754 and 414, to get
754 = 414 x 1 + 340
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 340 and 414, to get
414 = 340 x 1 + 74
Step 3: We consider the new divisor 340 and the new remainder 74, and apply the division lemma to get
340 = 74 x 4 + 44
We consider the new divisor 74 and the new remainder 44,and apply the division lemma to get
74 = 44 x 1 + 30
We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get
44 = 30 x 1 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 754 and 414 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(74,44) = HCF(340,74) = HCF(414,340) = HCF(754,414) .
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Frequently Asked Questions on HCF of 754, 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 754, 414?
Answer: HCF of 754, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.