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 347, 8177, 8932 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 347, 8177, 8932 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 347, 8177, 8932 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 347, 8177, 8932 is 1.
HCF(347, 8177, 8932) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 347, 8177, 8932 is 1.
Step 1: Since 8177 > 347, we apply the division lemma to 8177 and 347, to get
8177 = 347 x 23 + 196
Step 2: Since the reminder 347 ≠ 0, we apply division lemma to 196 and 347, to get
347 = 196 x 1 + 151
Step 3: We consider the new divisor 196 and the new remainder 151, and apply the division lemma to get
196 = 151 x 1 + 45
We consider the new divisor 151 and the new remainder 45,and apply the division lemma to get
151 = 45 x 3 + 16
We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get
45 = 16 x 2 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 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 347 and 8177 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(151,45) = HCF(196,151) = HCF(347,196) = HCF(8177,347) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8932 > 1, we apply the division lemma to 8932 and 1, to get
8932 = 1 x 8932 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8932 is 1
Notice that 1 = HCF(8932,1) .
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 347, 8177, 8932?
Answer: HCF of 347, 8177, 8932 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 347, 8177, 8932 using Euclid's Algorithm?
Answer: For arbitrary numbers 347, 8177, 8932 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.