Highest Common Factor of 663, 977, 45 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 663, 977, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 977, 45 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 663, 977, 45 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 663, 977, 45 is 1.
HCF(663, 977, 45) = 1
HCF of 663, 977, 45 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 977, 45 is 1.
Highest Common Factor of 663,977,45 is 1
Step 1: Since 977 > 663, we apply the division lemma to 977 and 663, to get
977 = 663 x 1 + 314
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 314 and 663, to get
663 = 314 x 2 + 35
Step 3: We consider the new divisor 314 and the new remainder 35, and apply the division lemma to get
314 = 35 x 8 + 34
We consider the new divisor 35 and the new remainder 34,and apply the division lemma to get
35 = 34 x 1 + 1
We consider the new divisor 34 and the new remainder 1,and apply the division lemma to get
34 = 1 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 663 and 977 is 1
Notice that 1 = HCF(34,1) = HCF(35,34) = HCF(314,35) = HCF(663,314) = HCF(977,663) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
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Frequently Asked Questions on HCF of 663, 977, 45 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 663, 977, 45?
Answer: HCF of 663, 977, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 977, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 977, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
