Highest Common Factor of 9960, 3435, 63742 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 9960, 3435, 63742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9960, 3435, 63742 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 9960, 3435, 63742 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 9960, 3435, 63742 is 1.
HCF(9960, 3435, 63742) = 1
HCF of 9960, 3435, 63742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9960, 3435, 63742 is 1.
Highest Common Factor of 9960,3435,63742 is 1
Step 1: Since 9960 > 3435, we apply the division lemma to 9960 and 3435, to get
9960 = 3435 x 2 + 3090
Step 2: Since the reminder 3435 ≠ 0, we apply division lemma to 3090 and 3435, to get
3435 = 3090 x 1 + 345
Step 3: We consider the new divisor 3090 and the new remainder 345, and apply the division lemma to get
3090 = 345 x 8 + 330
We consider the new divisor 345 and the new remainder 330,and apply the division lemma to get
345 = 330 x 1 + 15
We consider the new divisor 330 and the new remainder 15,and apply the division lemma to get
330 = 15 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 9960 and 3435 is 15
Notice that 15 = HCF(330,15) = HCF(345,330) = HCF(3090,345) = HCF(3435,3090) = HCF(9960,3435) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63742 > 15, we apply the division lemma to 63742 and 15, to get
63742 = 15 x 4249 + 7
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 7 and 15, to get
15 = 7 x 2 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 63742 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(63742,15) .
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Frequently Asked Questions on HCF of 9960, 3435, 63742 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 9960, 3435, 63742?
Answer: HCF of 9960, 3435, 63742 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9960, 3435, 63742 using Euclid's Algorithm?
Answer: For arbitrary numbers 9960, 3435, 63742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.