Highest Common Factor of 991, 356, 16 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, 356, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 991, 356, 16 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, 356, 16 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, 356, 16 is 1.
HCF(991, 356, 16) = 1
HCF of 991, 356, 16 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, 356, 16 is 1.
Highest Common Factor of 991,356,16 is 1
Step 1: Since 991 > 356, we apply the division lemma to 991 and 356, to get
991 = 356 x 2 + 279
Step 2: Since the reminder 356 ≠ 0, we apply division lemma to 279 and 356, to get
356 = 279 x 1 + 77
Step 3: We consider the new divisor 279 and the new remainder 77, and apply the division lemma to get
279 = 77 x 3 + 48
We consider the new divisor 77 and the new remainder 48,and apply the division lemma to get
77 = 48 x 1 + 29
We consider the new divisor 48 and the new remainder 29,and apply the division lemma to get
48 = 29 x 1 + 19
We consider the new divisor 29 and the new remainder 19,and apply the division lemma to get
29 = 19 x 1 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 991 and 356 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(29,19) = HCF(48,29) = HCF(77,48) = HCF(279,77) = HCF(356,279) = HCF(991,356) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 1, we apply the division lemma to 16 and 1, to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16 is 1
Notice that 1 = HCF(16,1) .
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Frequently Asked Questions on HCF of 991, 356, 16 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, 356, 16?
Answer: HCF of 991, 356, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 991, 356, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 991, 356, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.