Highest Common Factor of 70, 140, 666 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 70, 140, 666 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 70, 140, 666 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 70, 140, 666 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 70, 140, 666 is 2.
HCF(70, 140, 666) = 2
HCF of 70, 140, 666 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 70, 140, 666 is 2.
Highest Common Factor of 70,140,666 is 2
Step 1: Since 140 > 70, we apply the division lemma to 140 and 70, to get
140 = 70 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 70, the HCF of 70 and 140 is 70
Notice that 70 = HCF(140,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 666 > 70, we apply the division lemma to 666 and 70, to get
666 = 70 x 9 + 36
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 36 and 70, to get
70 = 36 x 1 + 34
Step 3: We consider the new divisor 36 and the new remainder 34, and apply the division lemma to get
36 = 34 x 1 + 2
We consider the new divisor 34 and the new remainder 2, and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 70 and 666 is 2
Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(70,36) = HCF(666,70) .
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Frequently Asked Questions on HCF of 70, 140, 666 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 70, 140, 666?
Answer: HCF of 70, 140, 666 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 70, 140, 666 using Euclid's Algorithm?
Answer: For arbitrary numbers 70, 140, 666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.