Highest Common Factor of 414, 738, 978 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 414, 738, 978 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 738, 978 is 6 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 414, 738, 978 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 414, 738, 978 is 6.
HCF(414, 738, 978) = 6
HCF of 414, 738, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 738, 978 is 6.
Highest Common Factor of 414,738,978 is 6
Step 1: Since 738 > 414, we apply the division lemma to 738 and 414, to get
738 = 414 x 1 + 324
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 324 and 414, to get
414 = 324 x 1 + 90
Step 3: We consider the new divisor 324 and the new remainder 90, and apply the division lemma to get
324 = 90 x 3 + 54
We consider the new divisor 90 and the new remainder 54,and apply the division lemma to get
90 = 54 x 1 + 36
We consider the new divisor 54 and the new remainder 36,and apply the division lemma to get
54 = 36 x 1 + 18
We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 414 and 738 is 18
Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(90,54) = HCF(324,90) = HCF(414,324) = HCF(738,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 18, we apply the division lemma to 978 and 18, to get
978 = 18 x 54 + 6
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 6 and 18, to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 978 is 6
Notice that 6 = HCF(18,6) = HCF(978,18) .
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Frequently Asked Questions on HCF of 414, 738, 978 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 414, 738, 978?
Answer: HCF of 414, 738, 978 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 738, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 738, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.