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 654, 327, 475, 87 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 327, 475, 87 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 654, 327, 475, 87 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 654, 327, 475, 87 is 1.
HCF(654, 327, 475, 87) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 327, 475, 87 is 1.
Step 1: Since 654 > 327, we apply the division lemma to 654 and 327, to get
654 = 327 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 327, the HCF of 654 and 327 is 327
Notice that 327 = HCF(654,327) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 475 > 327, we apply the division lemma to 475 and 327, to get
475 = 327 x 1 + 148
Step 2: Since the reminder 327 ≠ 0, we apply division lemma to 148 and 327, to get
327 = 148 x 2 + 31
Step 3: We consider the new divisor 148 and the new remainder 31, and apply the division lemma to get
148 = 31 x 4 + 24
We consider the new divisor 31 and the new remainder 24,and apply the division lemma to get
31 = 24 x 1 + 7
We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get
24 = 7 x 3 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 327 and 475 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(31,24) = HCF(148,31) = HCF(327,148) = HCF(475,327) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 87 > 1, we apply the division lemma to 87 and 1, to get
87 = 1 x 87 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 87 is 1
Notice that 1 = HCF(87,1) .
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 654, 327, 475, 87?
Answer: HCF of 654, 327, 475, 87 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 327, 475, 87 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 327, 475, 87 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.