Highest Common Factor of 978, 624, 57 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, 624, 57 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 624, 57 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, 624, 57 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, 624, 57 is 3.
HCF(978, 624, 57) = 3
HCF of 978, 624, 57 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, 624, 57 is 3.
Highest Common Factor of 978,624,57 is 3
Step 1: Since 978 > 624, we apply the division lemma to 978 and 624, to get
978 = 624 x 1 + 354
Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 354 and 624, to get
624 = 354 x 1 + 270
Step 3: We consider the new divisor 354 and the new remainder 270, and apply the division lemma to get
354 = 270 x 1 + 84
We consider the new divisor 270 and the new remainder 84,and apply the division lemma to get
270 = 84 x 3 + 18
We consider the new divisor 84 and the new remainder 18,and apply the division lemma to get
84 = 18 x 4 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 624 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(84,18) = HCF(270,84) = HCF(354,270) = HCF(624,354) = HCF(978,624) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57 > 6, we apply the division lemma to 57 and 6, to get
57 = 6 x 9 + 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 57 is 3
Notice that 3 = HCF(6,3) = HCF(57,6) .
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Frequently Asked Questions on HCF of 978, 624, 57 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, 624, 57?
Answer: HCF of 978, 624, 57 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 624, 57 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 624, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.