Highest Common Factor of 736, 17416 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 736, 17416 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 736, 17416 is 8 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 736, 17416 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 736, 17416 is 8.
HCF(736, 17416) = 8
HCF of 736, 17416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 736, 17416 is 8.
Highest Common Factor of 736,17416 is 8
Step 1: Since 17416 > 736, we apply the division lemma to 17416 and 736, to get
17416 = 736 x 23 + 488
Step 2: Since the reminder 736 ≠ 0, we apply division lemma to 488 and 736, to get
736 = 488 x 1 + 248
Step 3: We consider the new divisor 488 and the new remainder 248, and apply the division lemma to get
488 = 248 x 1 + 240
We consider the new divisor 248 and the new remainder 240,and apply the division lemma to get
248 = 240 x 1 + 8
We consider the new divisor 240 and the new remainder 8,and apply the division lemma to get
240 = 8 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 736 and 17416 is 8
Notice that 8 = HCF(240,8) = HCF(248,240) = HCF(488,248) = HCF(736,488) = HCF(17416,736) .
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Frequently Asked Questions on HCF of 736, 17416 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 736, 17416?
Answer: HCF of 736, 17416 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 736, 17416 using Euclid's Algorithm?
Answer: For arbitrary numbers 736, 17416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.