Highest Common Factor of 978, 414, 459 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 978, 414, 459 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 414, 459 is 3 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 978, 414, 459 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 978, 414, 459 is 3.
HCF(978, 414, 459) = 3
HCF of 978, 414, 459 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 414, 459 is 3.
Highest Common Factor of 978,414,459 is 3
Step 1: Since 978 > 414, we apply the division lemma to 978 and 414, to get
978 = 414 x 2 + 150
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 150 and 414, to get
414 = 150 x 2 + 114
Step 3: We consider the new divisor 150 and the new remainder 114, and apply the division lemma to get
150 = 114 x 1 + 36
We consider the new divisor 114 and the new remainder 36,and apply the division lemma to get
114 = 36 x 3 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 414 is 6
Notice that 6 = HCF(36,6) = HCF(114,36) = HCF(150,114) = HCF(414,150) = HCF(978,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 459 > 6, we apply the division lemma to 459 and 6, to get
459 = 6 x 76 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 459 is 3
Notice that 3 = HCF(6,3) = HCF(459,6) .
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Frequently Asked Questions on HCF of 978, 414, 459 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 978, 414, 459?
Answer: HCF of 978, 414, 459 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 414, 459 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 414, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
