Highest Common Factor of 988, 415, 258 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, 415, 258 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 415, 258 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 988, 415, 258 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, 415, 258 is 1.
HCF(988, 415, 258) = 1
HCF of 988, 415, 258 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, 415, 258 is 1.
Highest Common Factor of 988,415,258 is 1
Step 1: Since 988 > 415, we apply the division lemma to 988 and 415, to get
988 = 415 x 2 + 158
Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 158 and 415, to get
415 = 158 x 2 + 99
Step 3: We consider the new divisor 158 and the new remainder 99, and apply the division lemma to get
158 = 99 x 1 + 59
We consider the new divisor 99 and the new remainder 59,and apply the division lemma to get
99 = 59 x 1 + 40
We consider the new divisor 59 and the new remainder 40,and apply the division lemma to get
59 = 40 x 1 + 19
We consider the new divisor 40 and the new remainder 19,and apply the division lemma to get
40 = 19 x 2 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 1
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 988 and 415 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(40,19) = HCF(59,40) = HCF(99,59) = HCF(158,99) = HCF(415,158) = HCF(988,415) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 258 > 1, we apply the division lemma to 258 and 1, to get
258 = 1 x 258 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 258 is 1
Notice that 1 = HCF(258,1) .
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Frequently Asked Questions on HCF of 988, 415, 258 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, 415, 258?
Answer: HCF of 988, 415, 258 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 415, 258 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 415, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.