Highest Common Factor of 170, 765, 723, 18 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 170, 765, 723, 18 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 765, 723, 18 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 170, 765, 723, 18 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 170, 765, 723, 18 is 1.
HCF(170, 765, 723, 18) = 1
HCF of 170, 765, 723, 18 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 765, 723, 18 is 1.
Highest Common Factor of 170,765,723,18 is 1
Step 1: Since 765 > 170, we apply the division lemma to 765 and 170, to get
765 = 170 x 4 + 85
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 85 and 170, to get
170 = 85 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 85, the HCF of 170 and 765 is 85
Notice that 85 = HCF(170,85) = HCF(765,170) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 723 > 85, we apply the division lemma to 723 and 85, to get
723 = 85 x 8 + 43
Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 43 and 85, to get
85 = 43 x 1 + 42
Step 3: We consider the new divisor 43 and the new remainder 42, and apply the division lemma to get
43 = 42 x 1 + 1
We consider the new divisor 42 and the new remainder 1, and apply the division lemma to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 85 and 723 is 1
Notice that 1 = HCF(42,1) = HCF(43,42) = HCF(85,43) = HCF(723,85) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18 > 1, we apply the division lemma to 18 and 1, to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 18 is 1
Notice that 1 = HCF(18,1) .
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Frequently Asked Questions on HCF of 170, 765, 723, 18 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 170, 765, 723, 18?
Answer: HCF of 170, 765, 723, 18 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 765, 723, 18 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 765, 723, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.