Highest Common Factor of 988, 402, 542 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, 402, 542 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 402, 542 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, 402, 542 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, 402, 542 is 2.
HCF(988, 402, 542) = 2
HCF of 988, 402, 542 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, 402, 542 is 2.
Highest Common Factor of 988,402,542 is 2
Step 1: Since 988 > 402, we apply the division lemma to 988 and 402, to get
988 = 402 x 2 + 184
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 184 and 402, to get
402 = 184 x 2 + 34
Step 3: We consider the new divisor 184 and the new remainder 34, and apply the division lemma to get
184 = 34 x 5 + 14
We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get
34 = 14 x 2 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 988 and 402 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(184,34) = HCF(402,184) = HCF(988,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 542 > 2, we apply the division lemma to 542 and 2, to get
542 = 2 x 271 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 542 is 2
Notice that 2 = HCF(542,2) .
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Frequently Asked Questions on HCF of 988, 402, 542 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, 402, 542?
Answer: HCF of 988, 402, 542 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 402, 542 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 402, 542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.