Highest Common Factor of 490, 882, 749 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 490, 882, 749 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 490, 882, 749 is 7 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 490, 882, 749 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 490, 882, 749 is 7.
HCF(490, 882, 749) = 7
HCF of 490, 882, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 490, 882, 749 is 7.
Highest Common Factor of 490,882,749 is 7
Step 1: Since 882 > 490, we apply the division lemma to 882 and 490, to get
882 = 490 x 1 + 392
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 392 and 490, to get
490 = 392 x 1 + 98
Step 3: We consider the new divisor 392 and the new remainder 98, and apply the division lemma to get
392 = 98 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 98, the HCF of 490 and 882 is 98
Notice that 98 = HCF(392,98) = HCF(490,392) = HCF(882,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 98, we apply the division lemma to 749 and 98, to get
749 = 98 x 7 + 63
Step 2: Since the reminder 98 ≠ 0, we apply division lemma to 63 and 98, to get
98 = 63 x 1 + 35
Step 3: We consider the new divisor 63 and the new remainder 35, and apply the division lemma to get
63 = 35 x 1 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 98 and 749 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(63,35) = HCF(98,63) = HCF(749,98) .
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Frequently Asked Questions on HCF of 490, 882, 749 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 490, 882, 749?
Answer: HCF of 490, 882, 749 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 490, 882, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 490, 882, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.