Highest Common Factor of 977, 577, 892, 65 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, 577, 892, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 577, 892, 65 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, 577, 892, 65 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, 577, 892, 65 is 1.
HCF(977, 577, 892, 65) = 1
HCF of 977, 577, 892, 65 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, 577, 892, 65 is 1.
Highest Common Factor of 977,577,892,65 is 1
Step 1: Since 977 > 577, we apply the division lemma to 977 and 577, to get
977 = 577 x 1 + 400
Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 400 and 577, to get
577 = 400 x 1 + 177
Step 3: We consider the new divisor 400 and the new remainder 177, and apply the division lemma to get
400 = 177 x 2 + 46
We consider the new divisor 177 and the new remainder 46,and apply the division lemma to get
177 = 46 x 3 + 39
We consider the new divisor 46 and the new remainder 39,and apply the division lemma to get
46 = 39 x 1 + 7
We consider the new divisor 39 and the new remainder 7,and apply the division lemma to get
39 = 7 x 5 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 977 and 577 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(39,7) = HCF(46,39) = HCF(177,46) = HCF(400,177) = HCF(577,400) = HCF(977,577) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 892 > 1, we apply the division lemma to 892 and 1, to get
892 = 1 x 892 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 892 is 1
Notice that 1 = HCF(892,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 1, we apply the division lemma to 65 and 1, to get
65 = 1 x 65 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65 is 1
Notice that 1 = HCF(65,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 977, 577, 892, 65 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, 577, 892, 65?
Answer: HCF of 977, 577, 892, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 577, 892, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 577, 892, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.