Highest Common Factor of 977, 549, 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 977, 549, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 549, 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 977, 549, 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 977, 549, 16 is 1.
HCF(977, 549, 16) = 1
HCF of 977, 549, 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 977, 549, 16 is 1.
Highest Common Factor of 977,549,16 is 1
Step 1: Since 977 > 549, we apply the division lemma to 977 and 549, to get
977 = 549 x 1 + 428
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 428 and 549, to get
549 = 428 x 1 + 121
Step 3: We consider the new divisor 428 and the new remainder 121, and apply the division lemma to get
428 = 121 x 3 + 65
We consider the new divisor 121 and the new remainder 65,and apply the division lemma to get
121 = 65 x 1 + 56
We consider the new divisor 65 and the new remainder 56,and apply the division lemma to get
65 = 56 x 1 + 9
We consider the new divisor 56 and the new remainder 9,and apply the division lemma to get
56 = 9 x 6 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 977 and 549 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(56,9) = HCF(65,56) = HCF(121,65) = HCF(428,121) = HCF(549,428) = HCF(977,549) .
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 977, 549, 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 977, 549, 16?
Answer: HCF of 977, 549, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 549, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 549, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.