Highest Common Factor of 342, 564 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 342, 564 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 564 is 6 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 342, 564 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 342, 564 is 6.
HCF(342, 564) = 6
HCF of 342, 564 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 564 is 6.
Highest Common Factor of 342,564 is 6
Step 1: Since 564 > 342, we apply the division lemma to 564 and 342, to get
564 = 342 x 1 + 222
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 222 and 342, to get
342 = 222 x 1 + 120
Step 3: We consider the new divisor 222 and the new remainder 120, and apply the division lemma to get
222 = 120 x 1 + 102
We consider the new divisor 120 and the new remainder 102,and apply the division lemma to get
120 = 102 x 1 + 18
We consider the new divisor 102 and the new remainder 18,and apply the division lemma to get
102 = 18 x 5 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 342 and 564 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(102,18) = HCF(120,102) = HCF(222,120) = HCF(342,222) = HCF(564,342) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 342, 564 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 342, 564?
Answer: HCF of 342, 564 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 564 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 564 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.