Highest Common Factor of 469, 168, 370 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 469, 168, 370 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 469, 168, 370 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 469, 168, 370 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 469, 168, 370 is 1.
HCF(469, 168, 370) = 1
HCF of 469, 168, 370 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 469, 168, 370 is 1.
Highest Common Factor of 469,168,370 is 1
Step 1: Since 469 > 168, we apply the division lemma to 469 and 168, to get
469 = 168 x 2 + 133
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 133 and 168, to get
168 = 133 x 1 + 35
Step 3: We consider the new divisor 133 and the new remainder 35, and apply the division lemma to get
133 = 35 x 3 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 469 and 168 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(133,35) = HCF(168,133) = HCF(469,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 370 > 7, we apply the division lemma to 370 and 7, to get
370 = 7 x 52 + 6
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 6 and 7, to get
7 = 6 x 1 + 1
Step 3: We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 370 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(370,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 469, 168, 370 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 469, 168, 370?
Answer: HCF of 469, 168, 370 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 469, 168, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 469, 168, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.