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 548, 642, 997, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 548, 642, 997, 57 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 548, 642, 997, 57 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 548, 642, 997, 57 is 1.
HCF(548, 642, 997, 57) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 548, 642, 997, 57 is 1.
Step 1: Since 642 > 548, we apply the division lemma to 642 and 548, to get
642 = 548 x 1 + 94
Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 94 and 548, to get
548 = 94 x 5 + 78
Step 3: We consider the new divisor 94 and the new remainder 78, and apply the division lemma to get
94 = 78 x 1 + 16
We consider the new divisor 78 and the new remainder 16,and apply the division lemma to get
78 = 16 x 4 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 548 and 642 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(78,16) = HCF(94,78) = HCF(548,94) = HCF(642,548) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 997 > 2, we apply the division lemma to 997 and 2, to get
997 = 2 x 498 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 997 is 1
Notice that 1 = HCF(2,1) = HCF(997,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57 > 1, we apply the division lemma to 57 and 1, to get
57 = 1 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57 is 1
Notice that 1 = HCF(57,1) .
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 548, 642, 997, 57?
Answer: HCF of 548, 642, 997, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 548, 642, 997, 57 using Euclid's Algorithm?
Answer: For arbitrary numbers 548, 642, 997, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.