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 312, 896, 457, 188 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 896, 457, 188 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 312, 896, 457, 188 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 312, 896, 457, 188 is 1.
HCF(312, 896, 457, 188) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 896, 457, 188 is 1.
Step 1: Since 896 > 312, we apply the division lemma to 896 and 312, to get
896 = 312 x 2 + 272
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 272 and 312, to get
312 = 272 x 1 + 40
Step 3: We consider the new divisor 272 and the new remainder 40, and apply the division lemma to get
272 = 40 x 6 + 32
We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get
40 = 32 x 1 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 312 and 896 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(272,40) = HCF(312,272) = HCF(896,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 457 > 8, we apply the division lemma to 457 and 8, to get
457 = 8 x 57 + 1
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 1 and 8, to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 457 is 1
Notice that 1 = HCF(8,1) = HCF(457,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 188 > 1, we apply the division lemma to 188 and 1, to get
188 = 1 x 188 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 188 is 1
Notice that 1 = HCF(188,1) .
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 312, 896, 457, 188?
Answer: HCF of 312, 896, 457, 188 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 896, 457, 188 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 896, 457, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.