Highest Common Factor of 945, 402, 63 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 945, 402, 63 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 945, 402, 63 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 945, 402, 63 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 945, 402, 63 is 3.

HCF(945, 402, 63) = 3

HCF of 945, 402, 63 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 945, 402, 63 is 3.

Highest Common Factor of 945,402,63 using Euclid's algorithm

Highest Common Factor of 945,402,63 is 3

Step 1: Since 945 > 402, we apply the division lemma to 945 and 402, to get

945 = 402 x 2 + 141

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 141 and 402, to get

402 = 141 x 2 + 120

Step 3: We consider the new divisor 141 and the new remainder 120, and apply the division lemma to get

141 = 120 x 1 + 21

We consider the new divisor 120 and the new remainder 21,and apply the division lemma to get

120 = 21 x 5 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 945 and 402 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(120,21) = HCF(141,120) = HCF(402,141) = HCF(945,402) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 63 > 3, we apply the division lemma to 63 and 3, to get

63 = 3 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 63 is 3

Notice that 3 = HCF(63,3) .

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Frequently Asked Questions on HCF of 945, 402, 63 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 945, 402, 63?

Answer: HCF of 945, 402, 63 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 945, 402, 63 using Euclid's Algorithm?

Answer: For arbitrary numbers 945, 402, 63 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.