Highest Common Factor of 345, 972, 426 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 345, 972, 426 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 972, 426 is 3 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 345, 972, 426 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 345, 972, 426 is 3.
HCF(345, 972, 426) = 3
HCF of 345, 972, 426 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 972, 426 is 3.
Highest Common Factor of 345,972,426 is 3
Step 1: Since 972 > 345, we apply the division lemma to 972 and 345, to get
972 = 345 x 2 + 282
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 282 and 345, to get
345 = 282 x 1 + 63
Step 3: We consider the new divisor 282 and the new remainder 63, and apply the division lemma to get
282 = 63 x 4 + 30
We consider the new divisor 63 and the new remainder 30,and apply the division lemma to get
63 = 30 x 2 + 3
We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get
30 = 3 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 345 and 972 is 3
Notice that 3 = HCF(30,3) = HCF(63,30) = HCF(282,63) = HCF(345,282) = HCF(972,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 426 > 3, we apply the division lemma to 426 and 3, to get
426 = 3 x 142 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 426 is 3
Notice that 3 = HCF(426,3) .
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Frequently Asked Questions on HCF of 345, 972, 426 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 345, 972, 426?
Answer: HCF of 345, 972, 426 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 972, 426 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 972, 426 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.