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 390, 140, 740 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 390, 140, 740 is 10 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 390, 140, 740 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 390, 140, 740 is 10.
HCF(390, 140, 740) = 10
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 390, 140, 740 is 10.
Step 1: Since 390 > 140, we apply the division lemma to 390 and 140, to get
390 = 140 x 2 + 110
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 110 and 140, to get
140 = 110 x 1 + 30
Step 3: We consider the new divisor 110 and the new remainder 30, and apply the division lemma to get
110 = 30 x 3 + 20
We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 390 and 140 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(110,30) = HCF(140,110) = HCF(390,140) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 740 > 10, we apply the division lemma to 740 and 10, to get
740 = 10 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 740 is 10
Notice that 10 = HCF(740,10) .
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 390, 140, 740?
Answer: HCF of 390, 140, 740 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 390, 140, 740 using Euclid's Algorithm?
Answer: For arbitrary numbers 390, 140, 740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.