Highest Common Factor of 501, 827, 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 501, 827, 978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 501, 827, 978 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 501, 827, 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 501, 827, 978 is 1.
HCF(501, 827, 978) = 1
HCF of 501, 827, 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 501, 827, 978 is 1.
Highest Common Factor of 501,827,978 is 1
Step 1: Since 827 > 501, we apply the division lemma to 827 and 501, to get
827 = 501 x 1 + 326
Step 2: Since the reminder 501 ≠ 0, we apply division lemma to 326 and 501, to get
501 = 326 x 1 + 175
Step 3: We consider the new divisor 326 and the new remainder 175, and apply the division lemma to get
326 = 175 x 1 + 151
We consider the new divisor 175 and the new remainder 151,and apply the division lemma to get
175 = 151 x 1 + 24
We consider the new divisor 151 and the new remainder 24,and apply the division lemma to get
151 = 24 x 6 + 7
We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get
24 = 7 x 3 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 501 and 827 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(151,24) = HCF(175,151) = HCF(326,175) = HCF(501,326) = HCF(827,501) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 1, we apply the division lemma to 978 and 1, to get
978 = 1 x 978 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 978 is 1
Notice that 1 = HCF(978,1) .
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Frequently Asked Questions on HCF of 501, 827, 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 501, 827, 978?
Answer: HCF of 501, 827, 978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 501, 827, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 501, 827, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
