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 177, 62049 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 177, 62049 is 3 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 177, 62049 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 177, 62049 is 3.
HCF(177, 62049) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 177, 62049 is 3.
Step 1: Since 62049 > 177, we apply the division lemma to 62049 and 177, to get
62049 = 177 x 350 + 99
Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 99 and 177, to get
177 = 99 x 1 + 78
Step 3: We consider the new divisor 99 and the new remainder 78, and apply the division lemma to get
99 = 78 x 1 + 21
We consider the new divisor 78 and the new remainder 21,and apply the division lemma to get
78 = 21 x 3 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 177 and 62049 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(78,21) = HCF(99,78) = HCF(177,99) = HCF(62049,177) .
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 177, 62049?
Answer: HCF of 177, 62049 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 177, 62049 using Euclid's Algorithm?
Answer: For arbitrary numbers 177, 62049 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.