Highest Common Factor of 988, 274 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 988, 274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 274 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 988, 274 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 988, 274 is 2.
HCF(988, 274) = 2
HCF of 988, 274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 988, 274 is 2.
Highest Common Factor of 988,274 is 2
Step 1: Since 988 > 274, we apply the division lemma to 988 and 274, to get
988 = 274 x 3 + 166
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 166 and 274, to get
274 = 166 x 1 + 108
Step 3: We consider the new divisor 166 and the new remainder 108, and apply the division lemma to get
166 = 108 x 1 + 58
We consider the new divisor 108 and the new remainder 58,and apply the division lemma to get
108 = 58 x 1 + 50
We consider the new divisor 58 and the new remainder 50,and apply the division lemma to get
58 = 50 x 1 + 8
We consider the new divisor 50 and the new remainder 8,and apply the division lemma to get
50 = 8 x 6 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 988 and 274 is 2
Notice that 2 = HCF(8,2) = HCF(50,8) = HCF(58,50) = HCF(108,58) = HCF(166,108) = HCF(274,166) = HCF(988,274) .
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Frequently Asked Questions on HCF of 988, 274 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 988, 274?
Answer: HCF of 988, 274 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.