Highest Common Factor of 588, 740, 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 588, 740, 978 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 740, 978 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 588, 740, 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 588, 740, 978 is 2.
HCF(588, 740, 978) = 2
HCF of 588, 740, 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 588, 740, 978 is 2.
Highest Common Factor of 588,740,978 is 2
Step 1: Since 740 > 588, we apply the division lemma to 740 and 588, to get
740 = 588 x 1 + 152
Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 152 and 588, to get
588 = 152 x 3 + 132
Step 3: We consider the new divisor 152 and the new remainder 132, and apply the division lemma to get
152 = 132 x 1 + 20
We consider the new divisor 132 and the new remainder 20,and apply the division lemma to get
132 = 20 x 6 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 588 and 740 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(132,20) = HCF(152,132) = HCF(588,152) = HCF(740,588) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 4, we apply the division lemma to 978 and 4, to get
978 = 4 x 244 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 978 is 2
Notice that 2 = HCF(4,2) = HCF(978,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 588, 740, 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 588, 740, 978?
Answer: HCF of 588, 740, 978 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 740, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 740, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.