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 720, 7710, 7458 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 7710, 7458 is 6 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 720, 7710, 7458 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 720, 7710, 7458 is 6.
HCF(720, 7710, 7458) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 7710, 7458 is 6.
Step 1: Since 7710 > 720, we apply the division lemma to 7710 and 720, to get
7710 = 720 x 10 + 510
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 510 and 720, to get
720 = 510 x 1 + 210
Step 3: We consider the new divisor 510 and the new remainder 210, and apply the division lemma to get
510 = 210 x 2 + 90
We consider the new divisor 210 and the new remainder 90,and apply the division lemma to get
210 = 90 x 2 + 30
We consider the new divisor 90 and the new remainder 30,and apply the division lemma to get
90 = 30 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 720 and 7710 is 30
Notice that 30 = HCF(90,30) = HCF(210,90) = HCF(510,210) = HCF(720,510) = HCF(7710,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7458 > 30, we apply the division lemma to 7458 and 30, to get
7458 = 30 x 248 + 18
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 18 and 30, to get
30 = 18 x 1 + 12
Step 3: We consider the new divisor 18 and the new remainder 12, and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 7458 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(7458,30) .
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 720, 7710, 7458?
Answer: HCF of 720, 7710, 7458 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 7710, 7458 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 7710, 7458 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.