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, 9201 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 9201 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, 9201 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, 9201 is 1.
HCF(977, 9201) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 977, 9201 is 1.
Step 1: Since 9201 > 977, we apply the division lemma to 9201 and 977, to get
9201 = 977 x 9 + 408
Step 2: Since the reminder 977 ≠ 0, we apply division lemma to 408 and 977, to get
977 = 408 x 2 + 161
Step 3: We consider the new divisor 408 and the new remainder 161, and apply the division lemma to get
408 = 161 x 2 + 86
We consider the new divisor 161 and the new remainder 86,and apply the division lemma to get
161 = 86 x 1 + 75
We consider the new divisor 86 and the new remainder 75,and apply the division lemma to get
86 = 75 x 1 + 11
We consider the new divisor 75 and the new remainder 11,and apply the division lemma to get
75 = 11 x 6 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 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 9201 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(75,11) = HCF(86,75) = HCF(161,86) = HCF(408,161) = HCF(977,408) = HCF(9201,977) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 9201?
Answer: HCF of 977, 9201 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 9201 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 9201 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.