Highest Common Factor of 670, 784, 45 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 670, 784, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 784, 45 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 670, 784, 45 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 670, 784, 45 is 1.
HCF(670, 784, 45) = 1
HCF of 670, 784, 45 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 784, 45 is 1.
Highest Common Factor of 670,784,45 is 1
Step 1: Since 784 > 670, we apply the division lemma to 784 and 670, to get
784 = 670 x 1 + 114
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 114 and 670, to get
670 = 114 x 5 + 100
Step 3: We consider the new divisor 114 and the new remainder 100, and apply the division lemma to get
114 = 100 x 1 + 14
We consider the new divisor 100 and the new remainder 14,and apply the division lemma to get
100 = 14 x 7 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 670 and 784 is 2
Notice that 2 = HCF(14,2) = HCF(100,14) = HCF(114,100) = HCF(670,114) = HCF(784,670) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 2, we apply the division lemma to 45 and 2, to get
45 = 2 x 22 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 45 is 1
Notice that 1 = HCF(2,1) = HCF(45,2) .
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Frequently Asked Questions on HCF of 670, 784, 45 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 670, 784, 45?
Answer: HCF of 670, 784, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 784, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 784, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.