Highest Common Factor of 978, 420, 596 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, 420, 596 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 420, 596 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 978, 420, 596 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, 420, 596 is 2.
HCF(978, 420, 596) = 2
HCF of 978, 420, 596 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, 420, 596 is 2.
Highest Common Factor of 978,420,596 is 2
Step 1: Since 978 > 420, we apply the division lemma to 978 and 420, to get
978 = 420 x 2 + 138
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 138 and 420, to get
420 = 138 x 3 + 6
Step 3: We consider the new divisor 138 and the new remainder 6, and apply the division lemma to get
138 = 6 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 420 is 6
Notice that 6 = HCF(138,6) = HCF(420,138) = HCF(978,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 596 > 6, we apply the division lemma to 596 and 6, to get
596 = 6 x 99 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 596 is 2
Notice that 2 = HCF(6,2) = HCF(596,6) .
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Frequently Asked Questions on HCF of 978, 420, 596 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, 420, 596?
Answer: HCF of 978, 420, 596 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 420, 596 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 420, 596 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.