Highest Common Factor of 648, 714, 70 using Euclid's algorithm
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 648, 714, 70 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 714, 70 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 648, 714, 70 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 648, 714, 70 is 2.
HCF(648, 714, 70) = 2
HCF of 648, 714, 70 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 714, 70 is 2.
Highest Common Factor of 648,714,70 is 2
Step 1: Since 714 > 648, we apply the division lemma to 714 and 648, to get
714 = 648 x 1 + 66
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 66 and 648, to get
648 = 66 x 9 + 54
Step 3: We consider the new divisor 66 and the new remainder 54, and apply the division lemma to get
66 = 54 x 1 + 12
We consider the new divisor 54 and the new remainder 12,and apply the division lemma to get
54 = 12 x 4 + 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 648 and 714 is 6
Notice that 6 = HCF(12,6) = HCF(54,12) = HCF(66,54) = HCF(648,66) = HCF(714,648) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 6, we apply the division lemma to 70 and 6, to get
70 = 6 x 11 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 70 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(70,6) .
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Frequently Asked Questions on HCF of 648, 714, 70 using Euclid's Algorithm
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 648, 714, 70?
Answer: HCF of 648, 714, 70 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 714, 70 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 714, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.