Highest Common Factor of 69, 18, 32, 372 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 69, 18, 32, 372 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 69, 18, 32, 372 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 69, 18, 32, 372 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 69, 18, 32, 372 is 1.
HCF(69, 18, 32, 372) = 1
HCF of 69, 18, 32, 372 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 69, 18, 32, 372 is 1.
Highest Common Factor of 69,18,32,372 is 1
Step 1: Since 69 > 18, we apply the division lemma to 69 and 18, to get
69 = 18 x 3 + 15
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 15 and 18, to get
18 = 15 x 1 + 3
Step 3: We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 69 and 18 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(69,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 3, we apply the division lemma to 32 and 3, to get
32 = 3 x 10 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 32 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 372 > 1, we apply the division lemma to 372 and 1, to get
372 = 1 x 372 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 372 is 1
Notice that 1 = HCF(372,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 69, 18, 32, 372 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 69, 18, 32, 372?
Answer: HCF of 69, 18, 32, 372 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 69, 18, 32, 372 using Euclid's Algorithm?
Answer: For arbitrary numbers 69, 18, 32, 372 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.