Highest Common Factor of 977, 378, 645 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, 378, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 378, 645 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, 378, 645 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, 378, 645 is 1.
HCF(977, 378, 645) = 1
HCF of 977, 378, 645 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, 378, 645 is 1.
Highest Common Factor of 977,378,645 is 1
Step 1: Since 977 > 378, we apply the division lemma to 977 and 378, to get
977 = 378 x 2 + 221
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 221 and 378, to get
378 = 221 x 1 + 157
Step 3: We consider the new divisor 221 and the new remainder 157, and apply the division lemma to get
221 = 157 x 1 + 64
We consider the new divisor 157 and the new remainder 64,and apply the division lemma to get
157 = 64 x 2 + 29
We consider the new divisor 64 and the new remainder 29,and apply the division lemma to get
64 = 29 x 2 + 6
We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get
29 = 6 x 4 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 378 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(64,29) = HCF(157,64) = HCF(221,157) = HCF(378,221) = HCF(977,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get
645 = 1 x 645 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1
Notice that 1 = HCF(645,1) .
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Frequently Asked Questions on HCF of 977, 378, 645 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, 378, 645?
Answer: HCF of 977, 378, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 378, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 378, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
