Highest Common Factor of 554, 992, 111, 131 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 554, 992, 111, 131 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 554, 992, 111, 131 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 554, 992, 111, 131 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 554, 992, 111, 131 is 1.
HCF(554, 992, 111, 131) = 1
HCF of 554, 992, 111, 131 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 554, 992, 111, 131 is 1.
Highest Common Factor of 554,992,111,131 is 1
Step 1: Since 992 > 554, we apply the division lemma to 992 and 554, to get
992 = 554 x 1 + 438
Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 438 and 554, to get
554 = 438 x 1 + 116
Step 3: We consider the new divisor 438 and the new remainder 116, and apply the division lemma to get
438 = 116 x 3 + 90
We consider the new divisor 116 and the new remainder 90,and apply the division lemma to get
116 = 90 x 1 + 26
We consider the new divisor 90 and the new remainder 26,and apply the division lemma to get
90 = 26 x 3 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 554 and 992 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(90,26) = HCF(116,90) = HCF(438,116) = HCF(554,438) = HCF(992,554) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 2, we apply the division lemma to 111 and 2, to get
111 = 2 x 55 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 111 is 1
Notice that 1 = HCF(2,1) = HCF(111,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 131 > 1, we apply the division lemma to 131 and 1, to get
131 = 1 x 131 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 131 is 1
Notice that 1 = HCF(131,1) .
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Frequently Asked Questions on HCF of 554, 992, 111, 131 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 554, 992, 111, 131?
Answer: HCF of 554, 992, 111, 131 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 554, 992, 111, 131 using Euclid's Algorithm?
Answer: For arbitrary numbers 554, 992, 111, 131 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.