Highest Common Factor of 978, 291, 998 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, 291, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 291, 998 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 978, 291, 998 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, 291, 998 is 1.
HCF(978, 291, 998) = 1
HCF of 978, 291, 998 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, 291, 998 is 1.
Highest Common Factor of 978,291,998 is 1
Step 1: Since 978 > 291, we apply the division lemma to 978 and 291, to get
978 = 291 x 3 + 105
Step 2: Since the reminder 291 ≠ 0, we apply division lemma to 105 and 291, to get
291 = 105 x 2 + 81
Step 3: We consider the new divisor 105 and the new remainder 81, and apply the division lemma to get
105 = 81 x 1 + 24
We consider the new divisor 81 and the new remainder 24,and apply the division lemma to get
81 = 24 x 3 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 978 and 291 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(81,24) = HCF(105,81) = HCF(291,105) = HCF(978,291) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 998 > 3, we apply the division lemma to 998 and 3, to get
998 = 3 x 332 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 998 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(998,3) .
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Frequently Asked Questions on HCF of 978, 291, 998 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, 291, 998?
Answer: HCF of 978, 291, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 291, 998 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 291, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.