Highest Common Factor of 991, 554 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 991, 554 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 991, 554 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 991, 554 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 991, 554 is 1.
HCF(991, 554) = 1
HCF of 991, 554 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 991, 554 is 1.
Highest Common Factor of 991,554 is 1
Step 1: Since 991 > 554, we apply the division lemma to 991 and 554, to get
991 = 554 x 1 + 437
Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 437 and 554, to get
554 = 437 x 1 + 117
Step 3: We consider the new divisor 437 and the new remainder 117, and apply the division lemma to get
437 = 117 x 3 + 86
We consider the new divisor 117 and the new remainder 86,and apply the division lemma to get
117 = 86 x 1 + 31
We consider the new divisor 86 and the new remainder 31,and apply the division lemma to get
86 = 31 x 2 + 24
We consider the new divisor 31 and the new remainder 24,and apply the division lemma to get
31 = 24 x 1 + 7
We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get
24 = 7 x 3 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 991 and 554 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(31,24) = HCF(86,31) = HCF(117,86) = HCF(437,117) = HCF(554,437) = HCF(991,554) .
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Frequently Asked Questions on HCF of 991, 554 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 991, 554?
Answer: HCF of 991, 554 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 991, 554 using Euclid's Algorithm?
Answer: For arbitrary numbers 991, 554 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.