Highest Common Factor of 650, 403, 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 650, 403, 978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 650, 403, 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 650, 403, 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 650, 403, 978 is 1.
HCF(650, 403, 978) = 1
HCF of 650, 403, 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 650, 403, 978 is 1.
Highest Common Factor of 650,403,978 is 1
Step 1: Since 650 > 403, we apply the division lemma to 650 and 403, to get
650 = 403 x 1 + 247
Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 247 and 403, to get
403 = 247 x 1 + 156
Step 3: We consider the new divisor 247 and the new remainder 156, and apply the division lemma to get
247 = 156 x 1 + 91
We consider the new divisor 156 and the new remainder 91,and apply the division lemma to get
156 = 91 x 1 + 65
We consider the new divisor 91 and the new remainder 65,and apply the division lemma to get
91 = 65 x 1 + 26
We consider the new divisor 65 and the new remainder 26,and apply the division lemma to get
65 = 26 x 2 + 13
We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get
26 = 13 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 650 and 403 is 13
Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(91,65) = HCF(156,91) = HCF(247,156) = HCF(403,247) = HCF(650,403) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 13, we apply the division lemma to 978 and 13, to get
978 = 13 x 75 + 3
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 3 and 13, to get
13 = 3 x 4 + 1
Step 3: 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 13 and 978 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(978,13) .
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Frequently Asked Questions on HCF of 650, 403, 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 650, 403, 978?
Answer: HCF of 650, 403, 978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 650, 403, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 650, 403, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.