Highest Common Factor of 668, 978, 499 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 668, 978, 499 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 668, 978, 499 is 1 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 668, 978, 499 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 668, 978, 499 is 1.
HCF(668, 978, 499) = 1
HCF of 668, 978, 499 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 668, 978, 499 is 1.
Highest Common Factor of 668,978,499 is 1
Step 1: Since 978 > 668, we apply the division lemma to 978 and 668, to get
978 = 668 x 1 + 310
Step 2: Since the reminder 668 ≠ 0, we apply division lemma to 310 and 668, to get
668 = 310 x 2 + 48
Step 3: We consider the new divisor 310 and the new remainder 48, and apply the division lemma to get
310 = 48 x 6 + 22
We consider the new divisor 48 and the new remainder 22,and apply the division lemma to get
48 = 22 x 2 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 668 and 978 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(310,48) = HCF(668,310) = HCF(978,668) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 499 > 2, we apply the division lemma to 499 and 2, to get
499 = 2 x 249 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 499 is 1
Notice that 1 = HCF(2,1) = HCF(499,2) .
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Frequently Asked Questions on HCF of 668, 978, 499 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 668, 978, 499?
Answer: HCF of 668, 978, 499 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 668, 978, 499 using Euclid's Algorithm?
Answer: For arbitrary numbers 668, 978, 499 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.