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 740, 888, 44, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 740, 888, 44, 513 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 740, 888, 44, 513 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 740, 888, 44, 513 is 1.
HCF(740, 888, 44, 513) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 740, 888, 44, 513 is 1.
Step 1: Since 888 > 740, we apply the division lemma to 888 and 740, to get
888 = 740 x 1 + 148
Step 2: Since the reminder 740 ≠ 0, we apply division lemma to 148 and 740, to get
740 = 148 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 148, the HCF of 740 and 888 is 148
Notice that 148 = HCF(740,148) = HCF(888,740) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 148 > 44, we apply the division lemma to 148 and 44, to get
148 = 44 x 3 + 16
Step 2: Since the reminder 44 ≠ 0, we apply division lemma to 16 and 44, to get
44 = 16 x 2 + 12
Step 3: We consider the new divisor 16 and the new remainder 12, and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 148 and 44 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(44,16) = HCF(148,44) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 4, we apply the division lemma to 513 and 4, to get
513 = 4 x 128 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 513 is 1
Notice that 1 = HCF(4,1) = HCF(513,4) .
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 740, 888, 44, 513?
Answer: HCF of 740, 888, 44, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 740, 888, 44, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 740, 888, 44, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.