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 544, 138, 580, 74 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 544, 138, 580, 74 is 2 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 544, 138, 580, 74 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 544, 138, 580, 74 is 2.
HCF(544, 138, 580, 74) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 544, 138, 580, 74 is 2.
Step 1: Since 544 > 138, we apply the division lemma to 544 and 138, to get
544 = 138 x 3 + 130
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 130 and 138, to get
138 = 130 x 1 + 8
Step 3: We consider the new divisor 130 and the new remainder 8, and apply the division lemma to get
130 = 8 x 16 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 544 and 138 is 2
Notice that 2 = HCF(8,2) = HCF(130,8) = HCF(138,130) = HCF(544,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 580 > 2, we apply the division lemma to 580 and 2, to get
580 = 2 x 290 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 580 is 2
Notice that 2 = HCF(580,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 2, we apply the division lemma to 74 and 2, to get
74 = 2 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 74 is 2
Notice that 2 = HCF(74,2) .
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 544, 138, 580, 74?
Answer: HCF of 544, 138, 580, 74 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 544, 138, 580, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 544, 138, 580, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.